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In this paper, we develop a new method to obtain the accessibility of stochastic partial differential equations driven by additive pure jump noise. An important novelty of this paper is to allow the driving noises to be degenerate. As an application, for the first time, we obtain the accessibility of a class of stochastic equations driven by pure jump (possibly degenerate) noise, including stochastic 2D Navier-Stokes equations, stochastic Burgers equations, stochastic singular p-Laplace equations, and stochastic fast diffusion equations. As a further application, we establish the ergodicity of stochastic singular p-Laplace equations and stochastic fast diffusion equations driven by additive pure jump noise, and we remark that the driving noises could be Compound Poisson processes or Lévy processes with heavy tails. [ABSTRACT FROM AUTHOR]

Due to the intermittent and unstable nature of PV systems, maximum power point tracking (MPPT) of PV systems is necessary in practice. At the same time, PV cells are also shaded by objects such as trees and houses in the environment causing local shadows, so the Lévy flight particle swarm optimisation (LFPSO) is proposed in this paper. The random walk process of Lévy flight is added to the particle swarm optimisation (PSO) to increase the diversity of the search, which can avoid falling into local optimal solutions. The experimental simulation results show that the algorithm proposed in this paper can still accurately track the global maximum power in the case of partial shading, which well avoids falling into the local maximum power. The performance is much higher than the traditional maximum power point tracking algorithm, which improves the efficiency of the PV system. [ABSTRACT FROM AUTHOR]

In this paper, we study one-dimensional hyperbolic Anderson models (HAM) driven by space-time pure-jump Lévy white noise in a finite-variance setting. Motivated by recent active research on limit theorems for stochastic partial differential equations driven by Gaussian noises, we present the first study in this Lévy setting. In particular, we first establish the spatial ergodicity of the solution and then a quantitative central limit theorem (CLT) for the spatial averages of the solution to HAM in both Wasserstein distance and Kolmogorov distance, with the same rate of convergence. To achieve the first goal (i.e. spatial ergodicity), we exploit some basic properties of the solution and apply a Poincaré inequality in the Poisson setting, which requires delicate moment estimates on the Malliavin derivatives of the solution. Such moment estimates are obtained in a soft manner by observing a natural connection between the Malliavin derivatives of HAM and a HAM with Dirac delta velocity. To achieve the second goal (i.e. CLT), we need two key ingredients: (i) a univariate second-order Poincaré inequality in the Poisson setting that goes back to Last, Peccati, and Schulte (Probab. Theory Related Fields, 2016) and has been recently improved by Trauthwein (arXiv:2212.03782); (ii) aforementioned moment estimates of Malliavin derivatives up to second order. We also establish a corresponding functional CLT by (a) showing the convergence in finite-dimensional distributions and (b) verifying Kolmogorov's tightness criterion. Part (a) is made possible by a linearization trick and the univariate second-order Poincaré inequality, while part (b) follows from a standard moment estimate with an application of Rosenthal's inequality. [ABSTRACT FROM AUTHOR]

In order to overcome the difficulty of parameter tuning caused by the large lag and time-varying nonlinearity of the tank for lysozyme fermentation, a temperature control method based on LRWOA-LSTM-PID is proposed in this paper. Firstly, according to the intrinsic mechanism of the fermenter, a temperature mechanism model based on a dynamic equation is designed, which can better reflect the temperature changes in the fermenter. Secondly, a Proportional Integral Derivative (PID) parameter tuning method based on a Long-Short Term Memory Network (LSTM) is proposed, which takes advantage of the ability of LSTM to learn time sequence information and obtains the variation trend between error sequences under continuous time sampling, thereby adjusting network weights more reasonably and accelerating PID parameter tuning. Finally, a Whale Optimization Algorithm (WOA) based on the Lévy flight and random walk strategy (LRWOA) is proposed for the initialization of LSTM parameters; this algorithm has excellent optimization capabilities and overcomes the problem of LSTM falling into local optimal solutions prematurely during parameter randomization. The results show that the method proposed in this paper can achieve rapid tuning of PID parameters, thereby improving the convergence speed of the system and reducing system overshoot. [ABSTRACT FROM AUTHOR]

We aimed to improve the detection accuracy of laser methane sensors in expansive temperature application environments. In this paper, a large-scale dataset of the measured concentration of the sensor at different temperatures is established, and a temperature compensation model based on the ISSA-BP neural network is proposed. On the data side, a large-scale dataset of 15,810 sets of laser methane sensors with different temperatures and concentrations was established, and an Improved Isolation Forest algorithm was used to clean the large-scale data and remove the outliers in the dataset. On the modeling framework, a temperature compensation model based on the ISSA-BP neural network is proposed. The quasi-reflective learning, chameleon swarm algorithm, Lévy flight, and artificial rabbits optimization are utilized to improve the initialization of the sparrow population, explorer position, anti-predator position, and position of individual sparrows in each generation, respectively, to improve the global optimization seeking ability of the standard sparrow search algorithm. The ISSA-BP temperature compensation model far outperforms the four models, SVM, RF, BP, and PSO-BP, in model evaluation metrics such as MAE, MAPE, RMSE, and R-square for both the training and test sets. The results show that the algorithm in this paper can significantly improve the detection accuracy of the laser methane sensor under the wide temperature application environment. [ABSTRACT FROM AUTHOR]

A new test to detect the change-point in the quasi-autocorrelation coefficient (QAC) structure of a simple linear model with heavy-tailed series was developed. It is more general than previous approaches to the change-point problem in that it allows for the process with innovations in the domain of the attraction of a stable law with index κ (0 < κ < 2). Since the existing methods for QAC change detection are not satisfactory, we converted QAC change to mean change through the moving window method, which greatly improved the efficiency. Thus, the aim of this paper was to construct a ratio-typed test based on M-estimation for the testing of mean change. Under regular conditions, the asymptotic distribution under the no change null hypothesis was functional of a Wiener process, not that of a Lévy stable process. The divergent rate under the alternative hypothesis was also given. The simulation results demonstrate that the performances of our proposed tests were outstanding. Finally, the theoretical results were applied to an analysis of daily USD/CNY exchange rates with respect to QAC change. [ABSTRACT FROM AUTHOR]

This paper introduces a novel metaheuristic algorithm named the opposition-based cooperation search algorithm with Nelder–Mead (OCSANM). This enhanced algorithm builds upon the cooperation search algorithm (CSA) by incorporating opposition-based learning (OBL) and the Nelder–Mead simplex search method. The primary application of this algorithm is the design of a fractional-order proportional–integral–derivative (FOPID) controller for a buck converter system. A comprehensive evaluation is conducted using statistical boxplot analysis, nonparametric statistical tests and convergence response comparisons to assess the algorithm's performance and confirm its superiority over CSA. Furthermore, the FOPID-controlled buck converter system based on OCSANM is compared with two top-performing algorithms: one using a hybridized approach of Lévy flight distribution with simulated annealing (LFDSA) and the other employing the improved hunger games search (IHGS) algorithm. This comparison encompasses transient and frequency responses, performance indices and robustness analysis. The results reveal the notable advantages of the proposed OCSANM-based system, including 25.8% and 8.7% faster rise times, 26% and 8.8% faster settling times compared with the best-performing approaches, namely LFDSA and IHGS, respectively. In addition, the OCSANM-based system exhibits a 34.7% and 9.6% wider bandwidth than the existing approaches-based systems. Incorporating voltage and current responses of the buck converter's switched circuit with the OCSANM-based FOPID controller further underscores the algorithm's effectiveness. To provide a comprehensive assessment, the paper also compares the proposed approach's time and frequency domain responses with those of 17 other state-of-the-art approaches attempting to control buck converter systems similarly. These findings affirm the effectiveness of the OCSANM in designing FOPID controllers for buck converter systems. [ABSTRACT FROM AUTHOR]

To address the anti-swing issue of the payload in bridge cranes, Proportional–Integral–Derivative (PID) control is a commonly used method. However, parameter tuning of the PID controller relies on empirical knowledge and often leads to system overshoot. This paper proposes an Improved Sparrow Search Algorithm (ISSA) to optimize the gains of PID controllers, alleviating adverse effects on payload oscillation and trolley positioning during the operation of overhead cranes. First, tent map chaos mapping is introduced to initialize the sparrow population, enhancing the algorithm's global search capability. Then, by integrating sine and cosine concepts along with nonlinear learning factors, the updating mechanism of discoverer positions is dynamically adjusted, expediting the solving process. Finally, the Lévy flight strategy is employed to update follower positions, thereby enhancing the algorithm's local escape capability. Additionally, a fitness function containing overshoot penalties is proposed to address overshoot issues. Simulation results indicate that the overshoot rates of all algorithms remain less than 3%. Moreover, compared with the Sparrow Search Algorithm (SSA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), and Whale optimization Algorithm (WOA), the optimized PID control system with the ISSA algorithm exhibits superior control performance and possesses certain robustness and adaptability. [ABSTRACT FROM AUTHOR]

Temperature and humidity as the key factors affecting the storage and ripening of fruits and vegetables directly determine the quality of fruits and vegetables. In this paper, a temperature and humidity model was constructed based on an integrated device of controlled atmosphere storage and ripening. Aiming at the shortcomings of the temperature and humidity model such as large inertia, nonlinearity, and model uncertainty, a fuzzy‐PID controller based on the improved Lévy flight particle swarm algorithm (LFPSO) is proposed. Initially, a mathematical model of temperature and humidity is developed through mechanism research and parameter estimation. Subsequently, a temperature and humidity fuzzy‐PID control strategy is proposed for regulating temperature and humidity. An improved LFPSO is then introduced to optimize the key parameters of the fuzzy‐PID controller, such as the quantization factor and the scale factor. The superiority of the improved LFPSO algorithm is verified by comparing the test functions. Finally, the improved LFPSO‐fuzzy‐PID controller, fuzzy‐PID controller, and Smith‐PID controller are applied to the simulation model for comparison using the MATLAB Simulink simulation platform. The results show that the improved LFPSO‐fuzzy‐PID control algorithm has a good control effect in the temperature and humidity simulation system of controlled atmosphere (CA) ripening container, which provides a reference for solving the optimization problem of actual engineering design. Practical applications: In order to reduce the postharvest cold chain losses of fruits and vegetables, this paper proposes a containerized style device that combines fruits and vegetables storage and ripening for simplifying the losses caused by transshipment at cold chain nodes. Since temperature and humidity play a key role in fruits and vegetables storage and ripening, which directly affect the product quality, this paper establishes a complete mathematical model of CA ripening temperature and humidity system by combining mechanism modeling and parameter identification. In order to keep the temperature and humidity within the ideal range, Smith‐PID controller, fuzzy‐PID controller, and fuzzy‐PID control method based on improved Lévy flight particle swarm optimization are proposed to regulate the air conditioner and humidifier. The performance of three different types of controllers was tested on the MATLAB. The simulation results demonstrate that the improved LFPSO‐fuzzy‐PID controller is superior and more effective than Smith‐PID and fuzzy‐PID controllers. [ABSTRACT FROM AUTHOR]

Path planning is an important research direction in the field of robotics; however, with the advancement of modern science and technology, the study of efficient, stable, and safe path-planning technology has become a realistic need in the field of robotics research. This paper introduces an improved sparrow search algorithm (ISSA) with a fusion strategy to further improve the ability to solve challenging tasks. First, the sparrow population is initialized using circle chaotic mapping to enhance diversity. Second, the location update formula of the northern goshawk is used in the exploration phase to replace the sparrow search algorithm's location update formula in the security situation. This improves the discoverer model's search breadth in the solution space and optimizes the problem-solving efficiency. Third, the algorithm adopts the Lévy flight strategy to improve the global optimization ability, so that the sparrow jumps out of the local optimum in the later stage of iteration. Finally, the adaptive T-distribution mutation strategy enhances the local exploration ability in late iterations, thus improving the sparrow search algorithm's convergence speed. This was applied to the CEC2021 function set and compared with other standard intelligent optimization algorithms to test its performance. In addition, the ISSA was implemented in the path-planning problem of mobile robots. The comparative study shows that the proposed algorithm is superior to the SSA in terms of path length, running time, path optimality, and stability. The results show that the proposed method is more effective, robust, and feasible in mobile robot path planning. [ABSTRACT FROM AUTHOR]

Introduction: Eye movement is one of the cues used in human--machine interface technologies for predicting the intention of users. The developing application in eye movement event detection is the creation of assistive technologies for paralyzed patients. However, developing an effective classifier is one of the main issues in eye movement event detection. Methods: In this paper, bidirectional long short-term memory (BILSTM) is proposed along with hyperparameter tuning for achieving effective eye movement event classification. The Lévy flight and interactive crossoverbased reptile search algorithm (LICRSA) is used for optimizing the hyperparameters of BILSTM. The issues related to overfitting are avoided by using fuzzy data augmentation (FDA), and a deep neural network, namely, VGG- 19, is used for extracting features from eye movements. Therefore, the optimization of hyperparameters using LICRSA enhances the classification of eye movement events using BILSTM. Results and Discussion: The proposed BILSTM--LICRSA is evaluated by using accuracy, precision, sensitivity, F1-score, area under the receiver operating characteristic (AUROC) curve measure, and area under the precision--recall curve (AUPRC) measure for four datasets, namely, Lund2013, collected dataset, GazeBaseR, and UTMultiView. The gazeNet, human manual classification (HMC), and multi-source information-embedded approach (MSIEA) are used for comparison with the BILSTM--LICRSA. The F1-score of BILSTM--LICRSA for the GazeBaseR dataset is 98.99%, which is higher than that of the MSIEA. [ABSTRACT FROM AUTHOR]

First hitting times (FHTs) describe the time it takes a random "searcher" to find a "target" and are used to study timescales in many applications. FHTs have been well-studied for diffusive search, especially for small targets, which is called the narrow capture or narrow escape problem. In this paper, we study the FHT to small targets for a one-dimensional superdiffusive search described by a Lévy flight. By applying the method of matched asymptotic expansions to a fractional differential equation we obtain an explicit asymptotic expansion for the mean FHT (MFHT). For fractional order s ε (0, 1) (describing a (2s)-stable Lévy flight whose squared displacement scales as t1/s in time t) and targets of radius \varepsilon \ll 1, we show that the MFHT is order one for s ε (1/2, 1) and diverges as log(1/\varepsilon) for s = 1/2 and \varepsilon 2s 1 for s ε (0, 1/2). We then use our asymptotic results to identify the value of s ε (0, 1] which minimizes the average MFHT and find that (a) this optimal value of s vanishes for sparse targets and (b) the value s = 1/2 (corresponding to an inverse square Lévy search) is optimal in only very specific circumstances. We confirm our results by comparison to both deterministic numerical solutions of the associated fractional differential equation and stochastic simulations. [ABSTRACT FROM AUTHOR]

This paper studies a stochastic two-species Schoener's competitive model with Lévy jumps by the mean-reverting Ornstein-Uhlenbeck process. First, the biological implication of introducing the Ornstein-Uhlenbeck process is illustrated. After that, we show the existence and uniqueness of the global solution. Moment estimates for the global solution of the stochastic model are then given. Moreover, by constructing the Lyapunov function and applying Itô's formula and Chebyshev's inequality, it is found that the model is stochastic and ultimately bounded. In addition, we give sufficient conditions for the extinction of species. Finally, numerical simulations are employed to demonstrate the analytical results. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced whale optimization algorithm based on virtual force to optimize coverage and address the problem of uneven coverage during the deployment of underwater sensor networks. This method is guided by the Lévy flight and virtual force algorithms and adopts a differential mutation strategy based on random walks. This improves the fitness of the initial population and population richness of the algorithm. The effectiveness of this method was verified through simulation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal portfolio problem for a company that can invest in two risky assets, where a novel Lévy-process-driven model is constructed to describe the dynamics of the wealth process by using a constant elasticity of variance model and a jump-diffusion process. A delicately designed value function is proposed under the mean–variance criterion to reflect the optimal portfolio for the stochastic volatility model. By using the verification theorem, the desired optimal portfolio strategy is proposed by the solution to certain Hamilton–Jacobi–Bellman equations. Furthermore, the corresponding expressions are achieved by using the stochastic analysis theory. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed optimal portfolio strategy. [ABSTRACT FROM AUTHOR]

The Artificial Electric Field Algorithm (AEFA) stands out as a physics-inspired metaheuristic, drawing inspiration from Coulomb's law and electrostatic force; however, while AEFA has demonstrated efficacy, it can face challenges such as convergence issues and suboptimal solutions, especially in high-dimensional problems. To overcome these challenges, this paper introduces a modified version of AEFA, named mAEFA, which leverages the capabilities of Lévy flights, simulated annealing, and the Adaptive s-best Mutation and Natural Survivor Method (NSM) mechanisms. While Lévy flights enhance exploration potential and simulated annealing improves search exploitation, the Adaptive s-best Mutation and Natural Survivor Method (NSM) mechanisms are employed to add more diversity. The integration of these mechanisms in AEFA aims to expand its search space, enhance exploration potential, avoid local optima, and achieve improved performance, robustness, and a more equitable equilibrium between local intensification and global diversification. In this study, a comprehensive assessment of mAEFA is carried out, employing a combination of quantitative and qualitative measures, on a diverse range of 29 intricate CEC'17 constraint benchmarks that exhibit different characteristics. The practical compatibility of the proposed mAEFA is evaluated on five engineering benchmark problems derived from the civil, mechanical, and industrial engineering domains. Results from the mAEFA algorithm are compared with those from seven recently introduced metaheuristic algorithms using widely adopted statistical metrics. The mAEFA algorithm outperforms the LCA algorithm in all 29 CEC'17 test functions with 100% superiority and shows better results than SAO, GOA, CHIO, PSO, GSA, and AEFA in 96.6%, 96.6%, 93.1%, 86.2%, 82.8%, and 58.6% of test cases, respectively. In three out of five engineering design problems, mAEFA outperforms all the compared algorithms, securing second place in the remaining two problems. Results across all optimization problems highlight the effectiveness and robustness of mAEFA compared to baseline metaheuristics. The suggested enhancements in AEFA have proven effective, establishing competitiveness in diverse optimization problems. [ABSTRACT FROM AUTHOR]

With the development of the integration of aviation safety and artificial intelligence, research on the combination of risk assessment and artificial intelligence is particularly important in the field of risk management, but searching for an efficient and accurate risk assessment algorithm has become a challenge for the civil aviation industry. Therefore, an improved risk assessment algorithm (PS-AE-LSTM) based on long short-term memory network (LSTM) with autoencoder (AE) is proposed for the various supervised deep learning algorithms in flight safety that cannot adequately address the problem of the quality on risk level labels. Firstly, based on the normal distribution characteristics of flight data, a probability severity(PS)model is established to enhance the quality of risk assessment labels. Secondly, autoencoder is introduced to reconstruct the flight parameter data to improve the data quality. Finally, utilizing the time-series nature of flight data, a long and short-term memory network is used to classify the risk level and improve the accuracy of risk assessment. Thus, a risk assessment experiment was conducted to analyze a fleet landing phase dataset using the PS-AE-LSTM algorithm to assess the risk level associated with aircraft hard landing events. The results show that the proposed algorithm achieves an accuracy of 86.45% compared with seven baseline models and has excellent risk assessment capability. [ABSTRACT FROM AUTHOR]

With the continuous development of rail transportation worldwide, the safety and economy of metro trains have become essential standards. The door system is one of the most frequently used components in the process of train operation, so the fault rate is much higher than other systems. In view of the above problems, a preventive maintenance (PM) model for critical components of metro train door system is established based on reliability in this paper. Firstly, the Pareto chart analysis method and failure mode effect and criticality analysis method are adopted to determine that the lower retaining pin assembly and balanced pressing wheel are the main fault components in the door system. The parameter values of the three-parameter Weibull model of the door components are accurately obtained through the improved dung beetle optimizer algorithm, which provides an essential theoretical basis for optimizing preventive maintenance decisions. Secondly, a PM model of metro door components is established, and Lévy flight is added to PSO to enhance the optimization performance of the algorithm and solve the preventive maintenance model. Finally, the model is verified by sorting out the historical fault maintenance data of the metro door system in a city. The experimental results show that the PM strategy has economic, safety and task performance advantages compared to traditional maintenance methods. [ABSTRACT FROM AUTHOR]

The paper examines the valuation and hedging of life insurance obligations in the presence of mortality risk using the local risk-minimizing hedging approach. Roughly speaking, it is assumed that the lifetime of policyholders in an insurance portfolio is modeled by a point process whose stochastic intensity is controlled by a diffusion process. The stock price process is assumed to be a regime-switching Lévy process with non-zero regime-switching drift, where the parameters are assumed to depend on the economic states. Using the Föllmer–Schweizer decomposition, the main valuation and hedging results for a conditional payment process are determined. Some specific situations have been considered in which the local risk-minimizing strategies for a stream of liability payments or a unit-linked contract are presented. [ABSTRACT FROM AUTHOR]

In this paper, we study the speed of extinction of continuous state branching processes in subcritical Lévy environments. More precisely, when the associated Lévy process to the environment drifts to -8 and, under a suitable exponential change of measure (Esscher transform), the environment either drifts to -8 or oscillates. We extend recent results of Palau et al. (2016) and Li and Xu (2018), where the branching term is associated to a spectrally positive stable Lévy process and complement the recent article of Bansaye et al. (2021) where the critical case was studied. Our methodology combines a path analysis of the branching process together with its Lévy environment, fluctuation theory for Lévy processes and the asymptotic behaviour of exponential functionals of Lévy processes. As an application of the aforementioned results, we characterise the process conditioned to survival also known as the Q-process. [ABSTRACT FROM AUTHOR]

The paper considers dimensional synthesis of a path generator four-bar linkage by applying the modified Differential Evolution (DE) algorithm. During the search of the space, the DE algorithm may skip the right solution and lead to premature convergence. If the step is reduced, the search space is reduced as well, so that convergence becomes slower. Search efficiency may be achieved by including Lévy Flight in the DE algorithm. Namely, when the DE algorithm identifies the space of best solution, then a Levý Flight step is used for local search in that region, which significantly increases the exploitation capability and allows obtaining a very efficient solution of the optimization problem. The algorithm was tested with three examples of dimensional synthesis of a path generator four-bar linkage. The proposed algorithm can be very efficiently applied to solving very complex optimization problems. [ABSTRACT FROM AUTHOR]

This paper studies the Cramér–Lundberg asymptotics of the ruin probability for a model in which the reserve level process is described by a spectrally-positive light-tailed Markov additive process. By applying a change-of-measure technique in combination with elements from Wiener-Hopf theory, the exact asymptotics of the ruin probability are expressed in terms of the model primitives. In addition a simulation algorithm of generalized Siegmund type is presented, under which the returned estimate of the ruin probability has bounded relative error. Numerical experiments show that, compared to direct estimation, this algorithm greatly reduces the number of runs required to achieve an estimate with a given accuracy. The experiments also reveal that our asymptotic results provide a good approximation of the ruin probability even for relatively small initial surplus levels. [ABSTRACT FROM AUTHOR]

The paper suggests a hybrid numerical method to price barrier options under Levy processes. As the main ingredient of our approach, we model the values of the Wiener-Hopf factors using artificial neural networks in the exact formula for the solution. The numerical Wiener-Hopf factorization typically reduces the problem to the factorization of the polynomial of exp(iξ), which is interpreted as the characteristic function of the random variable that approximates the Lévy process at the exponentially distributed time moment. We design and train a feedforward neural network with one hidden layer that approximates the coefficients of factors based on the input vector of the factorized polynomial coefficients. We implemented in the software a training data generator and a generalized loss function to factorize a polynomial of arbitrary degree. We demonstrate the performance of our approach using examples of factorization of second-, sixth- and 254th-degree polynomials. It takes a fraction of a second for our trained artificial neural networks to calculate the factors. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the problem of reconstructing the past distribution for diffusion equations in multidimensional space with the presence of a poly-fractional operator which takes the following form$ {\mathbb{P}_\alpha }\left({{{\left({ - \Delta } \right)}^\gamma }} \right)u: = \sum\limits_{i = 1}^m {{\alpha _i}} {\left({ - \Delta } \right)^{{\gamma _i}}}u, $for $ m\in {\mathbb N} $, $ 0 < {\gamma _1} \le \cdots \le {\gamma _m} \le 1 $ and $ {\alpha _i} > 0 $ for $ i = \overline{1, m} $. The problem essentially arises from the superposition of multiple stochastic processes with different scales, including classical random walks and Lévy flights. We prove that the investigated problem is extremely ill-posed in the sense of Hadamard. Using an appropriate filtering method, we construct a regularized solution which converges to the original solution in $ L^2 $-sense. If we further impose a Gevrey-type a-priori condition, a Hölder convergence rate can be obtained. Three numerical examples using Matlab are also performed to demonstrate the ill-posedness of the problem and effectiveness of the regularization method. [ABSTRACT FROM AUTHOR]

This paper endeavours to directly establish the observability inequality of backward stochastic heat equations involving a Lévy process for measurable sets. As an immediate application, we attain the approximate controllability of forward stochastic heat equations featuring a Lévy process. Subsequently, we embark upon the formulation of a nuanced optimization problem, encompassing both the determination of an optimal actuator location and its associated minimum norm control. This formulation is elegantly cast as a two-person zero-sum game problem. We then proceed to articulate a set of conditions–both sufficient and necessary–required for optimizing the solution through the prism of a Nash equilibrium. At last, we prove that the relaxed optimal solution is an optimal actuator location for the classical problem. [ABSTRACT FROM AUTHOR]

The classical Liouville property says that all bounded harmonic functions in Rn$\mathbb {R}^n$, that is, all bounded functions satisfying Δf=0$\Delta f = 0$, are constant. In this paper, we obtain necessary and sufficient conditions on the symbol of a Fourier multiplier operator m(D)$m(D)$, such that the solutions f$f$ to m(D)f=0$m(D)f=0$ are Lebesgue a.e. constant (if f$f$ is bounded) or coincide Lebesgue a.e. with a polynomial (if f$f$ is polynomially bounded). The class of Fourier multipliers includes the (in general non‐local) generators of Lévy processes. For generators of Lévy processes, we obtain necessary and sufficient conditions for a strong Liouville theorem where f$f$ is positive and grows at most exponentially fast. As an application of our results above, we prove a coupling result for space‐time Lévy processes. [ABSTRACT FROM AUTHOR]

In this paper, we study McKean–Vlasov stochastic differential equations driven by Lévy processes. Firstly, under the non-Lipschitz condition which include classical Lipschitz conditions as special cases, we establish the existence and uniqueness for solutions of McKean–Vlasov stochastic differential equations using Carathéodory approximation. Then under certain averaging conditions, we establish a stochastic averaging principle for McKean–Vlasov stochastic differential equations driven by Lévy processes. We find that the solutions to stochastic systems concerned with Lévy noise can be approximated by solutions to averaged McKean–Vlasov stochastic differential equations driven by Lévy processes in the sense of convergence in p th moment. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of stochastic Riemann-Liouville type fractional differential equations driven by Lévy noise. By using Itô formula for the considered equation, we attempt to explore the non-confluence property of solution for the considered equation under some appropriate conditions. Our approach is to construct some suitable Lyapunov functions which is novel in exploring the non-confluence property of differential equations. [ABSTRACT FROM AUTHOR]

In response to the problems of easily falling into local optima, low path planning accuracy, and slow convergence speed when applying the traditional pelican optimization algorithm to the mobile robot path planning problem, a multi-strategy improved pelican optimization algorithm (MPOA) is proposed. In the initialization stage, chaotic mapping is used to increase the diversity of the pelican population individuals. In the exploration stage, an adaptive feedback adjustment factor is proposed to adjust the local optima of pelican individuals’ positions and balance the algorithm’s local development capability. In the development stage, the Lévy flight strategy is introduced to adjust the domain radius of the pelican population individuals, and the Gaussian mutation mechanism is used to disturb individuals that have fallen into local optima. Simulation experimental results show that the improved algorithm has significantly improved and effectively shortened the length of the planned path. [ABSTRACT FROM AUTHOR]

The paper develops a finite-time quantum state reduction framework via the use of Lévy random bridges (LRBs) that can be understood as Doob h-transformations on Lévy processes. Building upon the non-anticipative semimartingale representation of LRBs, we propose a family of energy-driven stochastic Schrödinger equations that go beyond the purely-continuous Brownian motion setup, and enter the scope of quantum systems involving discontinuities and heavy-tails. In doing so, we allow collapse dynamics to be governed intrinsically by the Markovian statistics of LRBs. The framework can host progressively convoluted stochastic state reduction dynamics in a tractable way and encapsulates jump-diffusion Schrödinger evolutions by use of the Lévy-Itô decomposition. Our construct motivates the usage of more general Markov processes and Doob h-transformations in producing consistent wave function collapse dynamics in finite-time. [ABSTRACT FROM AUTHOR]

The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time‐homogeneous case is classic, the time‐inhomogeneous case has recently received increased attention due to its added flexibility and advances in computational power. However, commuting sub‐intensity matrices are assumed, which in various cases limits the parsimonious properties of the resulting representation. This paper develops the theory required to solve the general case through maximum likelihood estimation, and in particular, using the expectation‐maximization algorithm. A reduction to a piecewise constant intensity matrix function is proposed in order to provide succinct representations, where a parametric linear model binds the intensities together. Practical aspects are discussed and illustrated through the estimation of notoriously demanding theoretical distributions and real data, from the perspective of matrix analytic methods. [ABSTRACT FROM AUTHOR]

A novel theoretical result on estimation of the local time and the occupation time measure of an α-stable Lévy process with α ∈ (1, 2) is presented. The approach is based upon computing the conditional expectation of the desired quantities given high frequency data, which is an L²-optimal statistic by construction. The corresponding stable central limit theorems are proved and a statistical application is discussed. In particular, this work extends the results of [20], which investigated the case of the Brownian motion. [ABSTRACT FROM AUTHOR]

• Feature selection is studied by a role-oriented binary grey wolf optimizer. • Foraging-following is combined with top grey wolves to improve convergence. • Lévy flight is integrated into ordinary grey wolves to improve population diversity. • The performance of feature selection is enhanced by more than 5%. • The performance of Improved algorithm is demonstrated by 29 benchmark functions. Feature selection can effectively define the feature subset, remove redundant, irrelevant, and noisy features. In order to adapt the feature selection problem, this paper adopts role-oriented modeling paradigm to make up for the defects of binary grey wolf optimizer such as premature, declining diversity, and insufficient convergence, then comes up with novel V-shaped linear transfer functions. Ultimately, a role-oriented binary grey wolf optimizer is proposed. The top grey wolves combine the foraging-following to enhance convergence, while the ordinary grey wolves integrate Lévy flight to avoid premature and improve diversity. The outstanding ability of role-oriented binary grey wolf optimizer in balance of exploitation and exploration is verified by benchmarks and the effectiveness in solving feature selection is demonstrated through feature selection tasks. The results of benchmark and feature selection task have comprehensively demonstrated the competitiveness of role-oriented modeling paradigm in improving metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

With view on global warming and the ongoing climate change, weather derivatives play an increasingly important role for many companies and financial investors, as they constitute useful hedging instruments against disadvantageous weather conditions. In this paper, we present a new temperature model based on generalized Langevin equations driven by Lévy processes. The proposed arithmetic approach captures numerous stylized facts of empirical temperature behavior like seasonal variations, time-dependent volatilities, memory effects, heavy tails and skewness. We further derive a representation for the related meteorological temperature forecast curve and infer the risk-neutral price dynamics of temperature derivatives like CAT, CDD and HDD futures. We finally deduce the minimal variance hedging portfolio in a specific temperature futures market by an application of a stochastic maximum principle and present several practical examples. [ABSTRACT FROM AUTHOR]

The butterfly optimization algorithm (BOA) is a meta-heuristic algorithm that mimics foraging and mating behavior of butterflies. In order to alleviate the problems of slow convergence, local optimum and lack of population diversity of BOA, an enhanced adaptive butterfly optimization algorithm (EABOA) is proposed in this paper. First, a new adaptive fragrance model is designed, which provided a finer fragrance perception way and effectively enhanced the convergence speed and accuracy. Second, Lévy flight with high-frequency short-step jumping and low-frequency long-step walking is adopted to help the algorithm jump out of the local optimum. Third, the dimension learning-based hunting is employed to enhance information exchange by creating neighbors for each butterfly, thus improving the balance between local and global search and maintaining population diversity. In addition, the Fitness-Distance-Constraint (FDC) method is introduced to enhance constraint handling in EABOA (named FDC-EABOA). The proposed EABOA is compared with 8 well-known algorithms and 8 BOA variants in CEC 2022 test suite and the results were statistically analyzed using Friedman, Friedman aligned rank, Wilcoxon signed rank, Quade rank and multiple comparisons, analysis of variance (ANOVA) and range analysis. Finally, EABOA and FDC-EABOA are applied to seven engineering problems (parameter identification of photovoltaic module model, speed reducer design, tension/compression spring design, pressure vessel design, gear train design, welded beam design, SOPWM for 3-level inverters), and metrics such as Improvement Index (IF) and Mean Constraint Violation (MV) confirm that the proposed algorithms are satisfactory. Experimental results and statistical analysis show that the proposed algorithms outperform the comparison algorithms and demonstrate the strong potential for solving numerical optimization and engineering design problems. [ABSTRACT FROM AUTHOR]

In this paper, we concentrate on the European option pricing problem in incomplete markets by taking Vasicek stochastic interest rate model into account and expanding it in accordance with a Lévy process named Variance Gamma (VG) process. In doing so, first, we prove the existence and uniqueness of the solution to the stochastic differential equation of this model. Then, by the means of the hedging and replicating techniques, pricing formulas for the bond and, in succession, for European options are established. Finally, from a numerical point of view, we will analyze the value of a bond based on our consideration model and also, we will study a European call option bond price. All these results are reported through the Monte-Carlo simulation method. [ABSTRACT FROM AUTHOR]

Transmission expansion planning (TEP) is a large-scale and complex problem. Recently, with the high penetration of renewable energy sources (RESs) into the power system, solving the TEP problems has become a challenge for many methodologies. In this paper, an improved zebra optimization algorithm (IZOA) is proposed to resolve the TEP problems with minimal total cost. In order to increase exploration ability, a Lévy flight function is added to the proposed IZOA method. In addition, the exploitation strategy is replaced with a function that does not depend on the number of interactions to help the search process not getting stuck in the local optimal values. The IEEE 24-bus RTS system with and without RESs is used to test the effectiveness of the proposed IZOA algorithm. The simulation results of IZOA are compared with the original ZOA and grey wolf optimization (GWO) method. In addition, to prove the robustness of the proposed method, IZOA is also compared with other existing methods, such as decision analysis (DA) and best-guided artificial bee colony algorithm (GABC), branch and bound (B&B), forensic based investigation optimization (FBIO) and symbiotic organisms Search (SOS). The simulation results show that the optimal value obtained by the proposed IZOA algorithm reduces 39.2% compared with the original ZOA, 36.4% for GWO, and 32.1 % for DA. Thus, the proposed algorithm is one of the suitable methods, powerful, and reliable techniques for solving the TEP problem with the penetration of RESs. [ABSTRACT FROM AUTHOR]

A novel position estimator is proposed to address the issue of position detection for micromanipulator in surgical robots. Firstly, the single joint micromanipulator experimental prototype proposed in the paper is built based on the real micromanipulator. To identify the parameters of the position estimator dynamics model, we enhance the Honey Badger Algorithm (HBA) and utilize Improved Honey Badger Algorithm (IHBA). With global parameters, the maximum absolute estimation error of the position estimator is only 1.10 deg. To further enhance position estimation accuracy, this paper introduces an online updating parameters model and integrates it with IHBA to achieve online updating parameters. The high-precision estimation of position estimator proposed in this paper is obtained. The experiments demonstrate the effective of the position estimator with maximum absolute estimation error is only 0.28 deg and the excellent robustness. • By incorporating the Lévy flight strategy and chaotic tent map, an improve HBA algorithm named IHBA is proposed. • An online updating parameters model is proposed and integrated with IHBA, significantly enhances the estimation accuracy of the position estimator. • A high-precision position estimator that accurately represents the performance of real micromanipulator is proposed. [ABSTRACT FROM AUTHOR]

To address the path planning problem for unmanned combat aerial vehicle (UCAV) more effectively, a novel two-stage path planning model is proposed. The first stage involves a longitudinal search primarily aimed at predicting the initial path, while the second stage is a horizontal search designed to correct the initial path. Furthermore, to tackle the UCAV path planning issue more effectively, this paper designs an improved elephant clan optimization (IECO) algorithm based on the average sample learning strategy, opposition-based learning, and Lévy flight disturbance strategy. Subsequently, IECO is integrated with the two-stage model (TSIECO) to address the UCAV path planning problem. Additionally, numerical experiments across 15 test functions reveal that IECO outperforms other algorithms in terms of optimization capability and convergence speed. Finally, the UCAV path planning experimental results indicate that the two-stage model based on IECO, as proposed in this paper, has significant advantages over traditional path planning models based on other swarm intelligence algorithms. Specifically, in three different simulated environments, the TSIECO has been tested on a total of 9 maps with varying parameters, yielding paths that are optimal in terms of cost and stability. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a non-linear Snell envelope which at each time represents the maximal value that can be achieved by stopping a BSDE with constrained jumps. We establish the existence of the Snell envelope by employing a penalization technique and the primary challenge we encounter is demonstrating the regularity of the limit for the scheme. Additionally, we relate the Snell envelope to a finite horizon, zero-sum stochastic differential game, where one player controls a path-dependent stochastic system by invoking impulses, while the opponent is given the opportunity to stop the game prematurely. Importantly, by developing new techniques within the realm of control randomization, we demonstrate that the value of the game exists and is precisely characterized by our non-linear Snell envelope. [ABSTRACT FROM AUTHOR]

• A novel method is proposed for multi-failure mode reliability analysis. • The utilization of two kinds of feedback mechanisms controls the search direction. • The computation cost of the proposed method is decreased by direction control. • The proposed method can balance computational efficiency and accuracy well. Searching for the most probable point (MPP) by traditional methods cannot avoid the demand for accurate gradients of limit state functions (LSFs) essentially. It is difficult to calculate the accurate gradient of unknown high nonlinear LSFs. In this paper, a multi-failure mode reliability analysis method based on intelligent directional search with constraint feedback (IDS) is proposed, focusing on unknown high nonlinear LSFs. (i): To improve the convergence rate, a point on the feasible domain boundary is settled as a starting point. The starting point is also located in the quadrant containing the MPP. (ii): To further enhance the optimization efficiency, the improved slime mould algorithm (iSMA) is proposed by adding constraint feedback, so that the current optimal point can move towards the LSF during the optimization process. (iii): To overcome the local optimum, iSMA and adaptive Lévy flight are combined which can expand the search area in the exploration phase. Finally, the failure probability of multi-failure mode is obtained by the second-order approximation method (SOAM) based on the MPPs. Three mathematical examples are utilized to demonstrate the excellent accuracy and acceptable efficiency of the proposed method by comparison with other existing methods. The results indicate that when the nonlinearity of LSF is not very high, IDS has the same computational cost as ECC, and the same order of accuracy as an intelligent optimization algorithm. As the nonlinearity of LSF of structural system failure modes increases, the computational cost of IDS will be higher than ECC. However, the accuracy of IDS has always been good enough. When the structural system has a concave LSF, IDS is more efficient than other intelligent optimization algorithms. Results of the engineering example indicate that the proposed method is very suitable for multi-failure mode reliability analysis problems with unknown high nonlinear LSF. [ABSTRACT FROM AUTHOR]

We derive methods for risk-neutral pricing of multi-asset options, when log-returns jointly follow a multivariate tempered stable distribution. These lead to processes that are more realistic than the better known Brownian motion and stable processes. Further, we introduce the diagonal tempered stable model, which is parsimonious but allows for rich dependence between assets. Here, the number of parameters only grows linearly as the dimension increases, which makes it tractable in higher dimensions and avoids the so-called "curse of dimensionality." As an illustration, we apply the model to price multi-asset options in two, three, and four dimensions. Detailed goodness-of-fit methods show that our model fits the data very well. [ABSTRACT FROM AUTHOR]

The recently introduced coati optimization algorithm suffers from drawbacks such as slow search velocity and weak optimization precision. An enhanced coati optimization algorithm called CMRLCCOA is proposed. Firstly, the Sine chaotic mapping function is used to initialize the CMRLCCOA as a way to obtain better-quality coati populations and increase the diversity of the population. Secondly, the generated candidate solutions are updated again using the convex lens imaging reverse learning strategy to expand the search range. Thirdly, the Lévy flight strategy increases the search step size, expands the search range, and avoids the phenomenon of convergence too early. Finally, utilizing the crossover strategy can effectively reduce the search blind spots, making the search particles constantly close to the global optimum solution. The four strategies work together to enhance the efficiency of COA and to boost the precision and steadiness. The performance of CMRLCCOA is evaluated on CEC2017 and CEC2019. The superiority of CMRLCCOA is comprehensively demonstrated by comparing the output of CMRLCCOA with the previously submitted algorithms. Besides the results of iterative convergence curves, boxplots and a nonparametric statistical analysis illustrate that the CMRLCCOA is competitive, significantly improves the convergence accuracy, and well avoids local optimal solutions. Finally, the performance and usefulness of CMRLCCOA are proven through three engineering application problems. A mathematical model of the hypersonic vehicle cruise trajectory optimization problem is developed. The result of CMRLCCOA is less than other comparative algorithms and the shortest path length for this problem is obtained. [ABSTRACT FROM AUTHOR]

The vibration signals of rolling bearings exhibit nonlinear and non-stationary characteristics under the influence of noise. In intelligent fault diagnosis, unprocessed signals will lead to weak fault characteristics and low diagnostic accuracy. To solve the above problem, a fault diagnosis method based on parameter optimization feature mode decomposition and improved deep belief networks is proposed. The feature mode decomposition is used to decompose the vibration signals. The parameter adaptation of feature mode decomposition is implemented by improved whale optimization algorithm including Levy flight strategy and adaptive weight. The selection of activation function and parameters is crucial in the application of deep belief networks. The improved deep belief networks are proposed based on Hard swish activation function and the improved whale optimization algorithm. The optimized diagnosis model is applied to weak fault diagnosis of bearings. The experimental results show that this method has faster convergence speed and anti-noise performance under the interference of −5 db noise, and effectively improves the adaptive feature extraction ability of the model and the accuracy of fault diagnosis. Under different conditions, the average accuracy reached 97.8% and 97.6%, with good generalization performance. [ABSTRACT FROM AUTHOR]

We developed a new method to price double barrier options under pure non-Gaussian Lévy processes admitting jumps of unbounded variation. In our approach, we represent the underlying process as a sequence of spectrally positive, negative, and again positive jumps, with spectrally positive jumps corresponding to half of the time moment. This rule is applied to the increments of the Lévy process at exponentially distributed time points. The justification for the convergence of the method in time is carried out using the interpretation of time randomization as the numerical Laplace transform inversion with the Post-Widder formula. The main algorithm consists of the recurrent calculation of the sufficient simple expectations of the intermediate price function depending on the position of the extremum of spectrally positive or negative part of the underying Lévy process at a randomized time moment. It corresponds to a sequence of problems for integro-differential equations on an interval, each of which is solved semi-explicitly by the Wiener–Hopf method. We decompose the characteristic function of a randomized spectrally positive (negative) process as the product of two Wiener–Hopf factors, the first of which corresponds to the exponential distribution and the second is calculated as a ratio. The parameter of the exponential distribution is numerically found as the only root of the factorizing operator symbol using Newton's method. Thus, by combining the sequential application of the Wiener–Hopf operators in explicit form with the characteristic function of our interval, we obtain the solution to each auxiliary problem. The main advantage of the suggested methods is that being very simple for programming it makes it possible to avoid dealing with Wiener–Hopf matrix factorization or solving systems of coupled nontrivial Wiener–Hopf equations that require application of tricky approximate factorization formulas. [ABSTRACT FROM AUTHOR]

The existence of density function of the running maximum of a stochastic differential equation (SDE) driven by a Brownian motion and a nontruncated pure-jump process is verified. This is proved by the existence of density function of the running maximum of the Wiener–Poisson functionals resulting from Bismut’s approach to the Malliavin calculus for jump processes. [ABSTRACT FROM AUTHOR]

This work proposes a novel stochastic model describing the propagation dynamics of the hepatitis B virus. The model takes into account numerous disease characteristics, and environmental disturbances were collected using Lévy jumps and the conventional Brownian motions. Initially, the deterministic model is developed, and the asymptotic behavior of the model's solution near the equilibria is examined. The deterministic model is transformed into a stochastic model while retaining the Lévy jumps and conventional Brownian motions. Under specific assumptions, the stochastic system is shown to have a unique solution. The study further investigates the conditions that ensure the extinction and persistence of the infection. The numerical solutions to both stochastic and deterministic systems were obtained using the well-known Milstein and RK4 techniques, and the analytical findings are theoretically confirmed. The simulation suggests that the noise intensities have a direct relationship with the amplitudes of the stochastic curves around the equilibria of the deterministic system. Smaller values of the intensities imply negligible fluctuations of trajectories around the equilibria and, hence, better describe the extinction and persistence of the infection. It has also been found that both Brownian motions and the Lévy jump had a significant influence on the oscillations of these curves. A discussion of the findings of the study reveals other important aspects as well as some future research guidelines. In short, this study proposes a novel stochastic model to describe the propagation dynamics of the hepatitis B virus. [ABSTRACT FROM AUTHOR]