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In this paper, we present several remarks on the paper by Yao et al. (citeyearcite.nine). The results presented in the present paper are interesting improvements on the main results of Yao et al. [ABSTRACT FROM AUTHOR]

The controlled autoregressive autoregressive moving average (CARARMA) models are of popularity to describe the evolution characteristics of dynamical systems. To overcome the identification obstacle resulting from colored noises, this paper studies the identification of the CARARMA models by forming an intermediate correlated noise model. In order to realize the real-time prediction function of the models, the on-line identification scheme is developed by constructing the dynamical objective functions based on the real-time sampled observations. Firstly, a rolling optimization cost function is built based on the observation at a single sampling instant to catch the modal information at a single time point and a generalized extended stochastic gradient (GESG) algorithm is proposed through the stochastic gradient optimization. Secondly, a rolling window cost function is built in accordance with the dynamical batch observations within data window by extending the proposed GESG algorithm and the multi-innovation generalized extended stochastic gradient algorithm is derived. Thirdly, from the perspective of theoretical analysis, the convergence proof of the proposed algorithm is provided based on the stochastic martingale convergence theory. Finally, the simulation analysis and comparison studies are provided to show the performance of the proposed algorithms. [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]

Meta-learning is a pivotal and potentially influential machine learning approach to solve challenging problems in reinforcement learning. However, the costly hyper-parameter tuning for training stability of meta-learning is a known shortcoming and currently a hotspot of research. This paper addresses this shortcoming by introducing an online and easily trainable hyper-parameter optimization approach, called Meta Parameters Learning via Meta-Learning (MPML), to combine online hyper-parameter adjustment scheme into meta-learning algorithm, which reduces the need to tune hyper-parameters. Specifically, a basic learning rate for each training task is put forward. Besides, the proposed algorithm dynamically adapts multiple basic learning rate and a shared meta-learning rate through conducting gradient descent alongside the initial optimization steps. In addition, the sensitivity with respect to hyper-parameter choices in the proposed approach are also discussed compared with model-agnostic meta-learning method. The experimental results on reinforcement learning problems demonstrate MPML algorithm is easy to implement and delivers more highly competitive performance than existing meta-learning methods on a diverse set of challenging control tasks. [ABSTRACT FROM AUTHOR]

We revisit two old and apparently little known papers by Basuev (Teoret Mat Fiz 37(1):130-134, , Teoret Mat Fiz 39(1):94-105, ) and show that the results contained there yield strong improvements on current lower bounds of the convergence radius of the Mayer series for continuous particle systems interacting via a very large class of stable and tempered potentials, which includes the Lennard-Jones type potentials. In particular we analyze the case of the classical Lennard-Jones gas under the light of the Basuev scheme and, using also some new results (Yuhjtman in J Stat Phys 160(6): 1684-1695, ) on this model recently obtained by one of us, we provide a new lower bound for the Mayer series convergence radius of the classical Lennard-Jones gas, which improves by a factor of the order 10 on the current best lower bound recently obtained in de Lima and Procacci (J Stat Phys 157(3):422-435, ). [ABSTRACT FROM AUTHOR]

It is pointed out that a general theorem presented in Yu Miao and Shoufang Xu's paper has a serious gap. In this small note, a counterexample for this theorem is provided exhibiting a triangular array of real numbers and a sequence of independent identically distributed random variables for which its conclusion fails. An reformulation of Yu Miao and Shoufang Xu's general theorem is performed making this statement true. [ABSTRACT FROM AUTHOR]

The analysis of oscillatory properties of fractional circuits is still an open problem due to the multi-valuedness and non-locality of fractional operators. In this paper, the complex path integral approach is applied to achieve the impulsive response of fractional order RLCα circuit, which possesses the advantages of high precision and fast convergence as well as providing a novel way to the theoretical analysis of fractional order RLCα circuit. On this basis, the order dependent oscillation criterion (critical damping criterion) for fractional order RLCα circuit is successfully solved by adopting dimensionless analysis, and verified by the above proposed high accurate algorithm. Lastly, two examples are provided to validate and to show the advantages of the above conclusions. It should be highlighted that the approaches and conclusions of this paper are important supplements to the fractional order equivalent circuit modellings, and have important application values in engineering, viscoelastic materials and some other fields. [ABSTRACT FROM AUTHOR]

In this paper, we first point out a gap in Yang (2012). Next, strong convergence theorem for the common solution for a finite family of φ -strongly accretive operator equations in Banach spaces is established without any bounded assumption, and we also give an example to show universality of the result of this paper, which improve and extend some recent results. [ABSTRACT FROM AUTHOR]

A multi-modal search space can be defined as having multiple attraction basins - each basin has a single local optimum which is reached from all points in that basin when greedy local search is used. Optimization in multi-modal search spaces can then be viewed as a two-phase process. The first phase is exploration in which the most promising attraction basin is identified. The second phase is exploitation in which the best solution (i.e. the local optimum) within the previously identified attraction basin is attained. The goal of thresheld convergence is to improve the performance of search techniques during the first phase of exploration. The effectiveness of thresheld convergence has been demonstrated through applications to existing metaheuristics such as particle swarm optimization and differential evolution, and through the development of novel metaheuristics such as minimum population search and leaders and followers. [ABSTRACT FROM AUTHOR]

The concept of q-rung orthopair neutrosophic set is introduced in this paper and fundamental properties of it are studied. Also the ordinary notion of topological space is extended to q-rung orthopair neutrosophic environment, as well as the fundamental concepts of convergence, continuity, compactness and Hausdorff topological space. All these generalizations are illustrated by suitable examples. [ABSTRACT FROM AUTHOR]

This paper investigates income convergence of Indian states in the post-reform period when markets played a greater role in resource allocation. We analyze stochastic convergence of relative per capita incomes of 19 states for the period 1994–2018 by employing a recently developed panel data approach controlling for structural breaks as smooth shifts. Smooth shifts are modelled using a more flexible Fourier approach that does not require identifying the number, date, and form of breaks. The empirical results, contrary to recent empirical findings, do not support evidence in favour of convergence in per capita income among Indian states. Poor infrastructure, lack of adequate financial development, and weak governance structure coupled with low total factor productivity growth seem to be responsible for the divergence of income. The findings suggest that development intervention in the post-reform period has neither been of the required order nor in the desired direction to help the lagging states to catch up with the leading ones. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new scheme for the integration of the periodic nonlinear Schrödinger equation and rigorously prove convergence rates at low regularity. The new integrator has decisive advantages over standard schemes at low regularity. In particular, it is able to handle initial data in Hs for 0 < s ≤ 1. The key feature of the integrator is its ability to distinguish between low and medium frequencies in the solution and to treat them differently in the discretization. This new approach requires a well-balanced filtering procedure which is carried out in Fourier space. The convergence analysis of the proposed scheme is based on discrete (in time) Bourgain space estimates which we introduce in this paper. A numerical experiment illustrates the superiority of the new integrator over standard schemes for rough initial data. [ABSTRACT FROM AUTHOR]

In this paper, we study the almost sure boundedness and the convergence of the stochastic approximation (SA) algorithm. At present, most available convergence proofs are based on the ODE method, and the almost sure boundedness of the iterations is an assumption and not a conclusion. In Borkar and Meyn (SIAM J Control Optim 38:447–469, 2000), it is shown that if the ODE has only one globally attractive equilibrium, then under additional assumptions, the iterations are bounded almost surely, and the SA algorithm converges to the desired solution. Our objective in the present paper is to provide an alternate proof of the above, based on martingale methods, which are simpler and less technical than those based on the ODE method. As a prelude, we prove a new sufficient condition for the global asymptotic stability of an ODE. Next we prove a "converse" Lyapunov theorem on the existence of a suitable Lyapunov function with a globally bounded Hessian, for a globally exponentially stable system. Both theorems are of independent interest to researchers in stability theory. Then, using these results, we provide sufficient conditions for the almost sure boundedness and the convergence of the SA algorithm. We show through examples that our theory covers some situations that are not covered by currently known results, specifically Borkar and Meyn (2000). [ABSTRACT FROM AUTHOR]

Aiming at the shortcomings of the traditional sparrow search algorithm (SSA) in path planning, such as its high time-consumption, long path length, it being easy to collide with static obstacles and its inability to avoid dynamic obstacles, this paper proposes a new improved SSA based on multi-strategies. Firstly, Cauchy reverse learning was used to initialize the sparrow population to avoid a premature convergence of the algorithm. Secondly, the sine–cosine algorithm was used to update the producers' position of the sparrow population and balance the global search and local exploration capabilities of the algorithm. Then, a Lévy flight strategy was used to update the scroungers' position to avoid the algorithm falling into the local optimum. Finally, the improved SSA and dynamic window approach (DWA) were combined to enhance the local obstacle avoidance ability of the algorithm. The proposed novel algorithm is named ISSA-DWA. Compared with the traditional SSA, the path length, path turning times and execution time planned by the ISSA-DWA are reduced by 13.42%, 63.02% and 51.35%, respectively, and the path smoothness is improved by 62.29%. The experimental results show that the ISSA-DWA proposed in this paper can not only solve the shortcomings of the SSA but can also plan a highly smooth path safely and efficiently in the complex dynamic obstacle environment. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish convergence and stability of Jungck -modified three-step iterations for three nonself mappings in a Banach space. The results obtained in this paper extend and improve the recent ones announced by Khan et al., Olatinwo, Hussain et al. and many papers. [ABSTRACT FROM AUTHOR]

This paper investigates the strong convergence of a fully discrete numerical method for the stochastic partial differential equations driven by multiplicative noise. The fully discrete space–time approximation consists of the symmetric interior penalty discontinuous Galerkin method for the spatial discretization and the implicit Euler method for the temporal discretization. Rather than the usual semi group analysis techniques, in this paper, we present an analysis framework in the variational formulation by introducing new weak variational approximation techniques. Some error estimates in a strong sense are established for the proposed fully discrete scheme. The optimal convergence rates are then obtained in both space and time. Numerical results for the nonlinear stochastic partial differential equations are finally presented to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we present a second-order accurate and linear numerical scheme for the phase field crystal equation and prove its convergence in the discrete L\infty sense. The key ingredient of the error analysis is to justify the boundedness of the numerical solution, so that the nonlinear term, treated explicitly in the scheme, can be bounded appropriately. Benefiting from the existence of the sixth-order dissipation term in the model, we first estimate the discrete H2 norm of the numerical error. The error estimate in the supremum norm is then obtained by the Sobolev embedding, so that the uniform bound of the numerical solution is available. We also show the mass conservation and the energy stability in the discrete setting. The proposed scheme is linear with constant coefficients so that it can be solved efficiently via some fast algorithms. Numerical experiments are conducted to verify the theoretical results, and long-time simulations in two- and three-dimensional spaces demonstrate the satisfactory and high effectiveness of the proposed numerical scheme. [ABSTRACT FROM AUTHOR]

In this paper, we introduced and studied the concept of lacunary statistical convergence of double sequence with respect to modulus function where the modulus function is an unbounded double sequence. We also introduced the concept of lacunary strong convergence of double sequence via modulus function. We further characterized those lacunary convergence of double sequence for which the lacunary statistically convergent of double sequence with respect to modulus function equals statistically convergent of double sequence with respect to modulus function. Finally, we established some inclusion relations between these two lacunary methods and proved some essential analogue for double sequence. [ABSTRACT FROM AUTHOR]

We consider inference problems for high‐dimensional (HD) functional data with a dense number of T repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal dependence, high dimensionality, and dense number of repeated measurements pose theoretical and computational challenges. This paper has two aims; our first aim is to solve the theoretical and computational challenges in testing equivalence among covariance matrices from HD functional data. The second aim is to provide computationally efficient and tuning‐free tools with guaranteed stochastic error control. The weak convergence of the stochastic process formed by the test statistics is established under the "large p, large T, and small n" setting. If the null is rejected, we further show that the locations of the change points can be estimated consistently. The estimator's rate of convergence is shown to depend on the data dimension, sample size, number of repeated measurements, and signal‐to‐noise ratio. We also show that our proposed computation algorithms can significantly reduce the computation time and are applicable to real‐world data with a large number of HD‐repeated measurements (e.g., functional magnetic resonance imaging (fMRI) data). Simulation results demonstrate both the finite sample performance and computational effectiveness of our proposed procedures. We observe that the empirical size of the test is well controlled at the nominal level, and the locations of multiple change points can be accurately identified. An application to fMRI data demonstrates that our proposed methods can identify event boundaries in the preface of the television series Sherlock. Code to implement the procedures is available in an R package named TechPhD. [ABSTRACT FROM AUTHOR]

In this paper, we establish new iterative methods for the solution of scalar equations by using the decomposition technique given in [16]. [ABSTRACT FROM AUTHOR]

In this paper, we apply the Adomian decomposition method (ADM) for solving Fractional Differential Equations (FDEs) with some modifications to the traditional method. The aim of this paper is to make ADM more efficient, rapid in convergence, and easy to use, so we will discuss two modifications. We use the reliable modification to simplify calculations. For difficulties in symbolic integration, we use a numerical implementation method. All these modifications were applied to the integer-order case, so we would apply it to FDEs. Some numerical results are given from solving these cases and comparing the solution with the ADM method. [ABSTRACT FROM AUTHOR]

We consider performing simulation experiments in the presence of covariates. Here, covariates refer to some input information other than system designs to the simulation model that can also affect the system performance. To make decisions, decision makers need to know the covariate values of the problem. Traditionally in simulation-based decision making, simulation samples are collected after the covariate values are known; in contrast, as a new framework, simulation with covariates starts the simulation before the covariate values are revealed and collects samples on covariate values that might appear later. Then, when the covariate values are revealed, the collected simulation samples are directly used to predict the desired results. This framework significantly reduces the decision time compared with the traditional way of simulation. In this paper, we follow this framework and suppose there are a finite number of system designs. We adopt the metamodel of stochastic kriging (SK) and use it to predict the system performance of each design and the best design. The goal is to study how fast the prediction errors diminish with the number of covariate points sampled. This is a fundamental problem in simulation with covariates and helps quantify the relationship between the offline simulation efforts and the online prediction accuracy. Particularly, we adopt measures of the maximal integrated mean squared error (IMSE) and integrated probability of false selection (IPFS) for assessing errors of the system performance and the best design predictions. Then, we establish convergence rates for the two measures under mild conditions. Last, these convergence behaviors are illustrated numerically using test examples. History: Accepted by Bruno Tuffin, area editor for simulation. Funding: This work was supported in part by Singapore Ministry of Education Academic Research Funds [Tier 1 Grants R-155-000-201-114 and A-0004822-00-00], the City University of Hong Kong [Grants 7005269 and 7005568], and the National Natural Science Foundation of China [Grant 72091211]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.1263) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0329) at (http://dx.doi.org/10.5281/zenodo.7344997). [ABSTRACT FROM AUTHOR]

This paper concerns the convergence of empirical measures in high dimensions. We propose a new class of probability metrics and show that under such metrics, the convergence is free of the curse of dimensionality (CoD). Such a feature is critical for high-dimensional analysis and stands in contrast to classical metrics (e.g. , the Wasserstein metric). The proposed metrics fall into the category of integral probability metrics, for which we specify criteria of test function spaces to guarantee the property of being free of CoD. Examples of the selected test function spaces include the reproducing kernel Hilbert spaces, Barron space, and flow-induced function spaces. Three applications of the proposed metrics are presented: 1. The convergence of empirical measure in the case of random variables; 2. The convergence of n -particle system to the solution to McKean–Vlasov stochastic differential equation; 3. The construction of an ɛ -Nash equilibrium for a homogeneous n -player game by its mean-field limit. As a byproduct, we prove that, given a distribution close to the target distribution measured by our metric and a certain representation of the target distribution, we can generate a distribution close to the target one in terms of the Wasserstein metric and relative entropy. Overall, we show that the proposed class of metrics is a powerful tool to analyze the convergence of empirical measures in high dimensions without CoD. [ABSTRACT FROM AUTHOR]

Initial conditions can have a substantial impact on the behavior of iterative root-finding techniques for nonlinear equations. By allowing complex starting points and complex roots, it is possible to examine the basins of attraction in the complex plane in order to compare the performance of various iterative techniques. In this paper, a one-parameter family of third-order root-finding methods is studied by varying its parameter A within −2.0 and 2.4 and applying it to a polynomial equation of high degree (degree 25). This family includes the Euler–Chebyshev's (A = 0), Halley's (A = 1) and BSC (A = 2) techniques. According to the results, the one-parameter family provides the best performance for values near A = 1, which equals to the Halley's method. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]

The vehicle routing problem with time windows (VRPTW) is a classical optimization problem. There have been many related studies in recent years. At present, many studies have generally analyzed this problem on the two-dimensional plane, and few studies have explored it on spherical surfaces. In order to carry out research related to the distribution of goods by unmanned vehicles and unmanned aerial vehicles, this study carries out research based on the situation of a three-dimensional sphere and proposes a three-dimensional spherical VRPTW model. All of the customer nodes in this problem were mapped to the three-dimensional sphere. The chimp optimization algorithm is an excellent intelligent optimization algorithm proposed recently, which has been successfully applied to solve various practical problems and has achieved good results. The chimp optimization algorithm (ChOA) is characterized by its excellent ability to balance exploration and exploitation in the optimization process so that the algorithm can search the solution space adaptively, which is closely related to its outstanding adaptive factors. However, the performance of the chimp optimization algorithm in solving discrete optimization problems still needs to be improved. Firstly, the convergence speed of the algorithm is fast at first, but it becomes slower and slower as the number of iterations increases. Therefore, this paper introduces the multiple-population strategy, genetic operators, and local search methods into the algorithm to improve its overall exploration ability and convergence speed so that the algorithm can quickly find solutions with higher accuracy. Secondly, the algorithm is not suitable for discrete problems. In conclusion, this paper proposes an improved chimp optimization algorithm (MG-ChOA) and applies it to solve the spherical VRPTW model. Finally, this paper analyzes the performance of this algorithm in a multi-dimensional way by comparing it with many excellent algorithms available at present. The experimental result shows that the proposed algorithm is effective and superior in solving the discrete problem of spherical VRPTW, and its performance is superior to that of other algorithms. [ABSTRACT FROM AUTHOR]

Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a certain number of steps of gradient or subgradient descent on each single objective at each iteration. In this paper, we show that stochastic alternating algorithms achieve a sublinear convergence rate of O (1 / T) , under strong convexity, for the determination of a minimizer of a weighted-sum of the two functions, parameterized by the number of steps applied on each of them. An extension to the convex case is presented for which the rate weakens to O (1 / T) . These rates are valid also in the non-smooth case. Importantly, by varying the proportion of steps applied to each function, one can determine an approximation to the Pareto front. [ABSTRACT FROM AUTHOR]

Real life problems are entrenched in ambiguities. To deal with these ambiguities, stochastic functional analysis has emerged as one of the mathematical tools for solving these kinds of problems. The purpose of this paper is to extend the convergence results of deterministic convex feasibility problems to a stochastic convex feasibility problem and prove that the solution of a convex feasibility problem generated by random Mann-type and Simultaneous projection iterative algorithms with firmly non-expansive mapping converge in quadratic mean and consequently in probability to random fixed point in Hilbert space. These results extend, unify, and generalize different established deterministic results in the literature. [ABSTRACT FROM AUTHOR]

After the discovery of the fractal structures of financial markets, enormous effort has been dedicated to finding accurate and stable numerical schemes to solve fractional Black-Scholes partial differential equations. This work, therefore, proposes a numerical scheme for pricing double-barrier options, written on an underlying stock whose dynamics are governed by a non-standard fractal stochastic process. The resultant model is time-fractional and is herein referred to as a time-fractional Black-Scholes model. The presence of the time-fractional derivative helps to capture the time-decaying effects of the underlying stock while capturing the globalized change in underlying prices and barriers. In this paper, we present the construction of the proposed scheme, analyse it in terms of its stability and convergence, and present two numerical examples of pricing double knock-in barrier-option problems. The results suggest that the proposed scheme is unconditionally stable and convergent with order O (h 2 + k 2) . [ABSTRACT FROM AUTHOR]

This paper is concerned with convergence of stochastic gradient algorithms with momentum terms in the nonconvex setting. A class of stochastic momentum methods, including stochastic gradient descent, heavy ball and Nesterov's accelerated gradient, is analyzed in a general framework under mild assumptions. Based on the convergence result of expected gradients, the authors prove the almost sure convergence by a detailed discussion of the effects of momentum and the number of upcrossings. It is worth noting that there are not additional restrictions imposed on the objective function and stepsize. Another improvement over previous results is that the existing Lipschitz condition of the gradient is relaxed into the condition of Hölder continuity. As a byproduct, the authors apply a localization procedure to extend the results to stochastic stepsizes. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the global minimization of a possibly non-smooth and nonconvex objective function constrained on the unit hypersphere by means of a multi-agent derivative-free method. The proposed algorithm falls into the class of the recently introduced consensus-based optimization. In fact, agents move on the sphere driven by a drift towards an instantaneous consensus point, which is computed as a convex combination of agent locations, weighted by the cost function according to Laplace's principle, and it represents an approximation to a global minimizer. The dynamics is further perturbed by an anisotropic random vector field to favor exploration. The main results of this paper are about the proof of convergence of the numerical scheme to global minimizers provided conditions of well-preparation of the initial datum. The proof of convergence combines a mean-field limit result with a novel asymptotic analysis and classical convergence results of numerical methods for stochastic differential equations. The main innovation with respect to previous work is the introduction of an anisotropic stochastic term, which allows us to ensure the independence of the parameters of the algorithm from the dimension and to scale the method to work in very high dimension. We present several numerical experiments, which show that the algorithm proposed in the present paper is extremely versatile and outperforms previous formulations with isotropic stochastic noise. [ABSTRACT FROM AUTHOR]

The subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept in applications of stochastic games, making it imperative to develop efficient methods to compute an SSPE. For this purpose, this paper develops an interior-point differentiable path-following method (IPM), which establishes a connection between an artificial logarithmic barrier game and the stochastic game of interest by adding a homotopy variable. IPM brings several advantages over the existing methods for stochastic games. On the one hand, IPM provides a bridge between differentiable path-following methods and interior-point methods and remedies several issues of an existing homotopy method called the stochastic linear tracing procedure (SLTP). First, the starting stationary strategy profile can be arbitrarily chosen. Second, IPM does not need switching between different systems of equations. Third, the use of a perturbation term makes IPM applicable to all stochastic games rather than generic games only. Moreover, a well-chosen transformation of variables reduces the number of equations and variables by roughly one half. Numerical results show that the proposed method is more than three times as efficient as SLTP. On the other hand, the stochastic game can be reformulated as a mixed complementarity problem and solved by the PATH solver. We employ the proposed IPM and the PATH solver to compute SSPEs. Numerical results evince that for some stochastic games the PATH solver may fail to find an SSPE, whereas IPM is successful in doing so for all stochastic games, which confirms the reliability and stability of the proposed method. Summary of Contribution: This paper incorporates the interior-point methods into a differentiable path-following method for computing stationary equilibria for stochastic games. This novel method brings excellent computational advantages and remedies several issues with the existing methods for stochastic games. We prove the global convergence of the proposed method and employ this method to solve numerous randomly generated stochastic games with different scales. Numerical results further confirm the high efficiency, stability, and universality of this method for stochastic games. [ABSTRACT FROM AUTHOR]

This paper proposes an extension of the model predictive control framework for switching continuous‐time linear systems. The switching times follow a stochastic process with limited statistical information. At each switching time, the controller knows the system state, but it is blind with respect to the switching continuous‐time subsystems. In this setting, the paper's main contribution is to show how to compute the model predictive control gain. The paper also illustrates the implications of our approach for applications. The approach was used in practice to control an electric current source that supplied a switching load. The experimental data support the usefulness of our approach. [ABSTRACT FROM AUTHOR]

This paper aims to examine convergence of income inequality in 21 OECD countries using several empirical techniques. In particular, we have used a new panel stationarity test, which allows for structural changes and cross-sectional dependence to examine the stochastic convergence of income inequality. We also employed a time series approach, residual augmented least squares-Lagrange multiplier unit root test. The empirical results show evidence for absolute, conditional, and sigma convergence. The conditional convergence test results suggest that countries are converging, but conditional on the two structural factors-economic and population growth. The stochastic convergence test results indicate the existence of convergence at the country-specific level. The results further confirm the existence of convergent clubs among OECD countries. [ABSTRACT FROM AUTHOR]

Due to the complex disjunctive structure of mathematical programs with complementarity constraints (MPCC), parametric approaches are used to overcome this difficulty. The underlying idea is to solve a program depending on the real parameter τ ≥ 0, where τ = 0 corresponds to the original MPCC program. The paper considers seven approaches: two based on smoothing the complementarity constraints and the other five, on their regularisation. We consider the point-to-set functions that, for each value of the parameter τ, define the set of feasible solutions and the set of optimal solution of the parametric problems they define. We study the distance between the feasible sets and the set of minimisers of the parametric program for τ going to zero. [ABSTRACT FROM AUTHOR]

In this paper, we propose a high-order nonlinear algorithm based on a finite difference method modification to the regularized long wave equation and the Benjamin–Bona–Mahony–Burgers equation subject to the homogeneous boundary. The consequence system of nonlinear equations typically trades with high computation burden. This dilemma can be overcome by establishing a fast numerical algorithm procedure without a reduction of numerical accuracy. The proposed algorithm forms a linear system with constant coefficient matrix at each time step and produces numerical solutions, which remarkably gains many computational advantages. In terms of analysis, a priori estimation for the numerical solution is derived to obtain the convergence and stability analysis. Additionally, the algorithm is globally mass preserving to avoid nonphysical behavior. Two benchmarks, including a single solitary wave to both equations, are given to validate the applicability and accuracy of the proposed method. Numerical results are obtained and compared to other approaches available in the literature. From the comparisons it is clear that the proposed approach produces accurate and precise results at low computational cost. Besides, the proposed scheme is applied to study the effect of the viscous term on a single solitary wave. It is shown that the viscous term results in the amplitude and width of the initial condition but not in its velocities in the case of a single solitary wave. As a consequence, theoretical and numerical findings provide a new area to investigate and expand the high-order algorithm for the family of wave equations. [ABSTRACT FROM AUTHOR]

In this paper we consider optimization problems with stochastic composite objective function subject to (possibly) infinite intersection of constraints. The objective function is expressed in terms of expectation operator over a sum of two terms satisfying a stochastic bounded gradient condition, with or without strong convexity type properties. In contrast to the classical approach, where the constraints are usually represented as intersection of simple sets, in this paper we consider that each constraint set is given as the level set of a convex but not necessarily differentiable function. Based on the exibility offered by our general optimization model we consider a stochastic subgradient method with random feasibility updates. At each iteration, our algorithm takes a stochastic proximal (sub)gradient step aimed at minimizing the objective function and then a subsequent subgradient step minimizing the feasibility violation of the observed random constraint. We analyze the convergence behavior of the proposed algorithm for diminishing stepsizes and for the case when the objective function is convex or has a quadratic functional growth, unifying the nonsmooth and smooth cases. We prove sublinear convergence rates for this stochastic subgradient algorithm, which are known to be optimal for subgradient methods on this class of problems. When the objective function has a linear least-square form and the constraints are polyhedral, it is shown that the algorithm converges linearly. Numerical evidence supports the effectiveness of our method in real problems. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop a method for proving almost sure convergence in the Gromov-Hausdorff-Prokhorov topology for a class of models of growing random graphs that generalises Rémy's algorithm for binary trees. We describe the obtained limits using some iterative gluing construction that generalises the famous line-breaking construction of Aldous' Brownian tree, and we characterize some of them using the self-similarity property in law that they satisfy. To do that, we develop a framework in which a metric space is constructed by gluing smaller metric spaces, called blocks, along the structure of a (possibly infinite) discrete tree. Our growing random graphs seen as metric spaces can be understood in this framework, that is, as evolving blocks glued along a growing discrete tree structure. Their scaling limit convergence can then be obtained by separately proving the almost sure convergence of every block and verifying some relative compactness property for the whole structure. For the particular models that we study, the discrete tree structure behind the construction has the distribution of an affine preferential attachment tree or a weighted recursive tree. We strongly rely on results concerning those two models and their connection, obtained in the companion paper Sénizergues (2021). [ABSTRACT FROM AUTHOR]

Given a probability distribution p := {pk}k=1∞ on the positive integers, there are two natural ways to construct a random permutation in Sn or a random permutation of N from IID samples from p. One is called the p-biased construction and the other the p-shifted construction. In the first part of the paper we consider the case that the distribution p is the geometric distribution with parameter 1 - q ∈ (0, 1). In this case, the p-shifted random permutation has the Mallows distribution with parameter q. Let Pnb;Geo(1-q) and Pns;Geo(1-q) denote the biased and the shifted distributions on Sn. The expected number of inversions of a permutation under Pns;Geo(1-q) is greater than under Pnb;Geo(1-q), and under either of these distributions, a permutation tends to have many fewer inversions than it would have under the uniform distribution. For fixed n, both Pnb;Geo(1-q) and Pns;Geo(1-q) converge weakly as q → 1 to the uniform distribution on Sn. We compare the biased and the shifted distributions by studying the inversion statistic under ... and ... for various rates of convergence of qn to 1. In the second part of the paper we consider p-biased and p-shifted permutations for the case that the distribution p is itself random and distributed as a GEM(θ)-distribution. In particular, in both the GEM(θ)-biased and the GEM(θ)-shifted cases, the expected number of inversions behaves asymptotically as it does under the Geo(1 - q)-shifted distribution with θ = q / 1-q . This allows one to consider the GEM(θ)-shifted case as the random counterpart of the Geo(q)-shifted case. We also consider another p-biased distribution with random p for which the expected number of inversions behaves asymptotically as it does under the Geo(1 - q)-biased case with θ and q as above, and with θ → ∞ and q → 1 [ABSTRACT FROM AUTHOR]

In this paper, we present the ideal convergence of triple sequences for rough variables. Furthermore, sequence convergence plays an extremely important role in the fundamental theory of mathematics. This paper presents two types of ideal convergence of rough triple sequence: Convergence in trust and convergence in mean. Some mathematical properties of those new convergence concepts are also given. In addition, we introduce ideal Cauchy triple sequence in rough spaces. [ABSTRACT FROM AUTHOR]

Due to the attractiveness of household gas-electric tools, in this paper, an optimization technique is suggested based on the integrated demand response (IDR) and degree of tolerance for household energy management. The proposed method is mostly used to express the dynamic change in the forms of energy and undetermined variables in the systems, resulting from household and photovoltaic (PV) load. Thermostatically controlled demands include gas-electricity and air conditioning, and cut-able loads include gas-electric stove and washing machine. The interval optimization is modeled for optimizing the operation and greenhouse gas emission costs in multi-purpose systems. The undetermined variables are formulated as interval statistics and the limitations are simplified by degree of tolerance. In order to solve it, the interval optimization technique is converted into certainty optimization with the interval order relationship and the delayed probability degree. Then, the developed grasshopper search algorithm is based on the chaos theory to solve the interval optimization model in order to respond to uncertainty and demands of the users, such that degree of tolerance of cost that is acceptable by users is optimized. Contrary to other optimization algorithms, the grasshopper search algorithm can be combined with other methods. In this paper, the chaos theory is adopted to find a better solution. Since the information is placed in the search space without order, using this technique considerably leads to good convergence speed, precise final solution finding, not being trapped in local minima, lower SD, and robustness. Both methods of IDR and degree of tolerance for the household gas-electric equipment manage to reduce energy consumption by about 25% compared to traditional methods. • Gas-electric equipment is integrated in household energy management. • A novel IDR method in HMES is proposed, while uncontrollable loads are also executed. • To deal with HMES uncertainty with electric equipment, interval optimization is used. • The users' degree of tolerance in HMES with gas-electric equipment is modeled. • New model of the GSA based on chaos theory is introduced. [ABSTRACT FROM AUTHOR]

In this paper, weak convergence of balanced stochastic one-step methods and especially balanced stochastic Runge–Kutta (SRK) methods for Itô multidimensional stochastic differential equations is analyzed. Generalizing a corresponding result obtained by H. Schurz for the standard Euler method, it is shown that under certain conditions, balanced one-step methods preserve the weak convergence properties of their underlying methods. As an application, this allows to prove the weak convergence order of the balanced SRK methods presented in earlier work by A. Rathinasamy, P. Nair and D. Ahmadian. [ABSTRACT FROM AUTHOR]

This article explores the convergence of cartography and robotic mapping, addressing key challenges and opportunities that arise as machines increasingly serve as both mapmakers and map users. The author investigates three critical questions: (1) how to best represent geographical data and maps for machines, (2) what dynamic information about our environment should be made readily available to machines, and (3) which ethical, religious, and cultural norms should be considered for autonomous entities. By addressing these questions, the author aims to facilitate the development of geospatial data representation, management, and analysis for autonomous systems, while ensuring harmonious coexistence with humans. In the scope of this paper, author tries to propose an approach to bridge the gap between traditional cartography and the emerging needs of machines as user and makers by building common ground through cross-disciplinary collaboration, joint research groups, and the development of common standards and frameworks. In this proposal, particularly by using design thinking approach, an event-mapping principle, as an approach that represents spatial information as events, is highlighted as a promising common framework for integrating static and dynamic spatial information. Since, event-based mapping and models can improve the representation of geographical data for machines, enabling them to better understand the environment and make informed decisions in complex and dynamic contexts. This convergence will ultimately transform the way we think about maps and geographical information systems in the age of machines. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Bernstein polynomial of the empirical distribution function F n under a triangular sample, which we denote by F ^ m , n . For the recentered and normalised statistic n 1 / 2 ( F ^ m , n (x) − E G n F ^ m , n (x)) , where x is defined on the interval (0 , 1) , the stochastic convergence to a Brownian bridge is derived. The main technicality in proving the normality is drawn off into a stochastic equicontinuity condition. To obtain the equicontinuity, we derive the uniform law of large numbers (ULLN) over a class of functions sup H | (P n − E G n ) h | by domination conditions of random covering numbers and covering integrals. In addition, we also derive the asymptotic covariance matrix for biavariant vector of Bernstein estimators. Finally, numerical simulations are presented to verify the validity of our main results. [ABSTRACT FROM AUTHOR]

The paper is dedicated to studying the problem of existence and uniqueness of solutions as well as existence of and exponential convergence to invariant measures for McKean-Vlasov stochastic differential equations with Markovian switching. Since the coefficients are only locally Lipschitz, we need to truncate them both in space and distribution variables simultaneously to get the global existence of solutions under the Lyapunov condition. Furthermore, if the Lyapunov condition is strengthened, we establish the exponential convergence of solutions' distributions to the unique invariant measure in Wasserstein quasi-distance and total variation distance, respectively. Finally, we give two applications to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Restoring images corrupted by Rician noise is a challenging issue in the field of medical image processing. In the existing variational methods, there is a balancing parameter between the regularization term and the fidelity term. However, it is very hard to find the optimal parameter. In this paper, we study the total variation-based Rician noise removal model with spatially varying parameters. We propose flexible and automatic parameter selection strategies to balance the regularization extent between different kinds of image regions. A modified alternating direction method of multipliers is derived to solve the non-convex model efficiently. Theoretically, we prove that if a selection strategy satisfies some reasonable conditions, the convergence of the proposed algorithm is guaranteed. Numerical results demonstrate that the proposed method with automatic parameter selection can better preserve the structures and fine textures than other closely related methods. [ABSTRACT FROM AUTHOR]