24 results on '"*STOCHASTIC integrals"'
Search Results
2. Dynamic risk measures via backward doubly stochastic Volterra integral equations with jumps.
- Author
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Chen, Yanhong and Miao, Liangliang
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VOLTERRA equations , *STOCHASTIC integrals - Abstract
In this article, we study dynamic risk measures by means of backward doubly stochastic Volterra integral equations (BDSVIEs, for short) with jumps. We establish the well-posedness of BDSVIEs with jumps in the sense of M-solution and prove a comparison theorem of BDSVIEs with jumps. Finally, we study properties of dynamic risk measures induced by BDSVIEs with jumps. Our results extend the well-posedness and the comparison theorem of BDSVIEs without jumps to the setting with jumps, and extend dynamic risk measures induced by BSDEs, BDSDEs, and BSVIEs to the case of BDSVIEs with jumps. [ABSTRACT FROM AUTHOR]
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- 2024
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3. When to efficiently rebalance a portfolio.
- Author
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Ando, Masayuki and Fukasawa, Masaaki
- Abstract
A constant weight asset allocation is a popular investment strategy and is optimal under a suitable continuous model. We study the tracking error for the target continuous rebalancing strategy by a feasible discrete-in-time rebalancing under a general multi-dimensional Brownian semimartingale model of asset prices. In a high-frequency asymptotic framework, we derive an asymptotically efficient sequence of simple predictable strategies. [ABSTRACT FROM AUTHOR]
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- 2024
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4. Lagrange interpolation polynomials for solving nonlinear stochastic integral equations.
- Author
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Boukhelkhal, Ikram and Zeghdane, Rebiha
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VOLTERRA equations , *NONLINEAR equations , *NEWTON-Raphson method , *COLLOCATION methods , *STOCHASTIC integrals , *JACOBI polynomials , *NONLINEAR integral equations - Abstract
In this article, an accurate computational approaches based on Lagrange basis and Jacobi-Gauss collocation method is suggested to solve a class of nonlinear stochastic Itô-Volterra integral equations (SIVIEs). Since the exact solutions of this kind of equations are not still available, so finding an accurate approximate solutions has attracted the interest of many scholars. In the proposed methods, using Lagrange polynomials and zeros of Jacobi polynomials, the considered system of linear and nonlinear stochastic Volterra integral equations is reduced to linear and nonlinear systems of algebraic equations. Solving the resulting algebraic systems by Newton's methods, approximate solutions of the stochastic Volterra integral equations are constructed. Theoretical study is given to validate the error and convergence analysis of these methods; the spectral rate of convergence for the proposed method is established in the L ∞ -norm. Several related numerical examples with different simulations of Brownian motion are given to prove the suitability and accuracy of our methods. The numerical experiments of the proposed methods are compared with the results of other numerical techniques. [ABSTRACT FROM AUTHOR]
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- 2024
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5. Generalized location-scale mixtures of elliptical distributions: Definitions and stochastic comparisons.
- Author
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Pu, Tong, Zhang, Yiying, and Yin, Chuancun
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STOCHASTIC integrals , *STOCHASTIC orders , *DISTRIBUTION (Probability theory) , *LINEAR orderings , *ACTUARIAL science - Abstract
This article proposes a unified class of generalized location-scale mixture of multivariate elliptical distributions and studies integral stochastic orderings of random vectors following such distributions. Given a random vector Z, independent of X and Y, the scale parameter of this class of distributions is mixed with a function α (Z) and its skew parameter is mixed with another function β (Z). Sufficient (and necessary) conditions are established for stochastically comparing different random vectors stemming from this class of distributions by means of several stochastic orders including the usual stochastic order, convex order, increasing convex order, supermodular order, and some related linear orders. Two insightful assumptions for the density generators of elliptical distributions, aiming to control the generators' tail, are provided to make stochastic comparisons among mixed-elliptical vectors. Some applications in applied probability and actuarial science are also provided as illustrations on the main findings. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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6. Weighted averaged Gaussian quadrature rules for modified Chebyshev measures.
- Author
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Djukić, Dušan Lj., Mutavdžić Djukić, Rada M., Reichel, Lothar, and Spalević, Miodrag M.
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JACOBI operators , *STOCHASTIC integrals - Abstract
This paper is concerned with the approximation of integrals of a real-valued integrand over the interval [ − 1 , 1 ] by Gauss quadrature. The averaged and optimal averaged quadrature rules ([13,21]) provide a convenient method for approximating the error in the Gauss quadrature. However, they are applicable to all integrands that are continuous on the interval [ − 1 , 1 ] only if their nodes are internal, i.e. if they belong to this interval. We discuss two approaches to determine averaged quadrature rules with nodes in [ − 1 , 1 ] : (i) truncating the Jacobi matrix associated with the optimal averaged rule, and (ii) weighting the optimal averaged quadrature rule. We consider Chebyshev measures of the first, second, and third kinds that are modified by a linear over linear rational factor, and discuss the internality of averaged, optimal averaged, and truncated optimal averaged quadrature rules. Moreover, we show that the weighting yields internal averaged rules if a weighting parameter is properly chosen, and we provide bounds for this parameter that guarantee internality. Finally, we illustrate that the weighted averaged rules give more accurate estimates of the quadrature error than the truncated optimal averaged rules. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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7. Connection probabilities of multiple FK-Ising interfaces.
- Author
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Feng, Yu, Peltola, Eveliina, and Wu, Hao
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CONFORMAL field theory , *PROBABILITY theory , *STATISTICAL correlation , *STOCHASTIC integrals , *PARTITION functions - Abstract
We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight q ∈ [ 1 , 4) . Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values of q than the FK-Ising model ( q = 2 ). Given the convergence of interfaces, the conjectural formulas for other values of q could be verified similarly with relatively minor technical work. The limit interfaces are variants of SLE κ curves (with κ = 16 / 3 for q = 2 ). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all q ∈ [ 1 , 4) , thus providing further evidence of the expected CFT description of these models. [ABSTRACT FROM AUTHOR]
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- 2024
- Full Text
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8. Stochastic Volterra equations with time-changed Lévy noise and maximum principles.
- Author
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di Nunno, Giulia and Giordano, Michele
- Subjects
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VOLTERRA equations , *STOCHASTIC differential equations , *NOISE , *NATURAL resources , *STOCHASTIC integrals - Abstract
Motivated by a problem of optimal harvesting of natural resources, we study a control problem for Volterra type dynamics driven by time-changed Lévy noises, which are in general not Markovian. To exploit the nature of the noise, we make use of different kind of information flows within a maximum principle approach. For this we work with backward stochastic differential equations (BSDE) with time-change and exploit the non-anticipating stochastic derivative introduced in Di Nunno and Eide (Stoch Anal Appl 28:54-85, 2009). We prove both a sufficient and necessary stochastic maximum principle. [ABSTRACT FROM AUTHOR]
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- 2024
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9. A representation theorem for set-valued submartingales.
- Author
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T. Tuyen, Luc and T. Luan, Vu
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PROBABILITY theory , *STOCHASTIC integrals , *INTEGRAL representations , *MARTINGALES (Mathematics) , *RANDOM sets , *STOCHASTIC processes - Abstract
The integral representation theorem for martingales has been widely used in probability theory. In this work, we propose and prove a general representation theorem for a class of set-valued submartingales. We also extend the stochastic integral representation for non-trivial initial set-valued martingales. Moreover, we show that this result covers the existing ones in the literature for both degenerated and non-degenerated set-valued martingales. [ABSTRACT FROM AUTHOR]
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- 2024
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10. Functional Solutions of Stochastic Differential Equations.
- Author
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van den Berg, Imme
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STOCHASTIC differential equations , *STOCHASTIC integrals , *DIFFERENTIAL equations , *FUNCTIONAL differential equations , *PARTIAL differential equations , *ORDINARY differential equations - Abstract
We present an integration condition ensuring that a stochastic differential equation d X t = μ (t , X t) d t + σ (t , X t) d B t , where μ and σ are sufficiently regular, has a solution of the form X t = Z (t , B t) . By generalizing the integration condition we obtain a class of stochastic differential equations that again have a functional solution, now of the form X t = Z (t , Y t) , with Y t an Ito process. These integration conditions, which seem to be new, provide an a priori test for the existence of functional solutions. Then path-independence holds for the trajectories of the process. By Green's Theorem, it holds also when integrating along any piece-wise differentiable path in the plane. To determine Z at any point (t , x) , we may start at the initial condition and follow a path that is first horizontal and then vertical. Then the value of Z can be determined by successively solving two ordinary differential equations. Due to a Lipschitz condition, this value is unique. The differential equations relate to an earlier path-dependent approach by H. Doss, which enables the expression of a stochastic integral in terms of a differential process. [ABSTRACT FROM AUTHOR]
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- 2024
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11. A projection method based on the piecewise Chebyshev cardinal functions for nonlinear stochastic ABC fractional integro‐differential equations.
- Author
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Heydari, M. H., Zhagharian, Sh., and Cattani, C.
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NONLINEAR functions , *STOCHASTIC integrals , *ALGEBRAIC equations , *INTEGRO-differential equations , *CAPUTO fractional derivatives , *MATRICES (Mathematics) , *FRACTIONAL differential equations - Abstract
In this study, the Atangana–Baleanu fractional derivative in the Caputo type (as a kind of non‐local and non‐singular derivative) is used to define a new class of stochastic fractional integro‐differential equations. A projection method (more precisely, a Galerkin approach) based on the piecewise Chebyshev cardinal functions is developed to solve these stochastic fractional equations. To construct this method, the operational matrices of fractional and stochastic integrals of these basis functions are obtained and used in the established method. By approximating the solution of the problem with a finite expansion of the expressed basis functions (in which the expansion coefficients are unknown), a system of algebraic equations is obtained. By solving this system, the expansion coefficients and subsequently the solution of the original stochastic fractional problem are obtained. The convergence analysis of the proposed method is investigated, theoretically and numerically. The accuracy of the established procedure is illustrated by solving several numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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12. Nearly unstable integer‐valued ARCH process and unit root testing.
- Author
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Barreto‐Souza, Wagner and Chan, Ngai Hang
- Subjects
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ASYMPTOTIC distribution , *TIME series analysis , *LIMIT theorems , *DEATH rate , *STOCHASTIC integrals , *TOPOLOGY , *ERROR rates , *MONTE Carlo method - Abstract
This paper introduces a Nearly Unstable INteger‐valued AutoRegressive Conditional Heteroscedastic (NU‐INARCH) process for dealing with count time series data. It is proved that a proper normalization of the NU‐INARCH process weakly converges to a Cox–Ingersoll–Ross diffusion in the Skorohod topology. The asymptotic distribution of the conditional least squares estimator of the correlation parameter is established as a functional of certain stochastic integrals. Numerical experiments based on Monte Carlo simulations are provided to verify the behavior of the asymptotic distribution under finite samples. These simulations reveal that the nearly unstable approach provides satisfactory and better results than those based on the stationarity assumption even when the true process is not that close to nonstationarity. A unit root test is proposed and its Type‐I error and power are examined via Monte Carlo simulations. As an illustration, the proposed methodology is applied to the daily number of deaths due to COVID‐19 in the United Kingdom. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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13. Backward doubly stochastic differential equations driven by fractional Brownian motion with stochastic integral-Lipschitz coefficients.
- Author
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Ndiaye, Assane, Aidara, Sadibou, and Sow, Ahmadou Bamba
- Subjects
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FRACTIONAL differential equations , *STOCHASTIC differential equations , *BROWNIAN motion , *STOCHASTIC integrals - Abstract
This paper deals with a class of backward doubly stochastic differential equations driven by fractional Brownian motion with Hurst parameter H greater than 1 2 . We essentially establish the existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients and stochastic integral-Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral. [ABSTRACT FROM AUTHOR]
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- 2024
- Full Text
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14. BSDEs driven by fractional Brownian motion with time-delayed generators.
- Author
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Aidara, Sadibou and Sylla, Lamine
- Subjects
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BROWNIAN motion , *STOCHASTIC differential equations , *STOCHASTIC integrals , *FRACTIONAL differential equations , *MOVING average process , *TIME perspective - Abstract
This paper deals with a class of backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1/2) with time-delayed generators. In this type of equation, a generator at time t can depend on the values of a solution in the past, weighted with a time-delay function, for instance, of the moving average type. We establish an existence and uniqueness result of solutions for a sufficiently small time horizon or for a sufficiently small Lipschitz constant of a generator. The stochastic integral used throughout the paper is the divergence operator-type integral. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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15. Lagrangian stochastic integrals of motion in isotropic random flows.
- Author
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Sirota, V. A., Il'yn, A. S., Kopyev, A. V., and Zybin, K. P.
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STOCHASTIC integrals , *INTEGRALS - Abstract
A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow and can be expressed in terms of local surface densities. The expression for the integrals is universal: it represents general geometric properties and does not depend on the statistics of the specific flow. [ABSTRACT FROM AUTHOR]
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- 2024
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16. Adaptive state feedback control of output‐constrained stochastic nonlinear systems with stochastic integral input‐to‐state stability inverse dynamics.
- Author
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Xie, Ruiming and Xu, Shengyuan
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STATE feedback (Feedback control systems) , *STOCHASTIC systems , *ADAPTIVE fuzzy control , *STOCHASTIC integrals , *CLOSED loop systems , *ADAPTIVE control systems , *NONLINEAR systems , *NONLINEAR functions - Abstract
This article studies the adaptive state‐feedback control problem of output‐constrained stochastic high‐order nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics. A key nonlinear transformation function is constructed to convert the original output‐constrained stochastic nonlinear system into an equivalent form without any output constraint. By subtly using the SiISS small‐gain condition and fully extracting the characteristics of system nonlinearities, two new control design and analysis methods are developed to guarantee that the closed‐loop system has an almost surely unique solution, all the closed‐loop signals are bounded almost surely, and the equilibrium point is stable in probability without the violation of output constraint. A simulation result is provided to show the effectiveness of this control method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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17. Stochastic calculus for tempered fractional Brownian motion and stability for SDEs driven by TFBM.
- Author
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Zhang, Lijuan, Wang, Yejuan, and Hu, Yaozhong
- Subjects
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BROWNIAN motion , *STOCHASTIC integrals , *STOCHASTIC differential equations , *FRACTIONAL calculus , *MALLIAVIN calculus - Abstract
The objective of this article is to introduce and study Itô type stochastic integrals with respect to tempered fractional Brownian motion (TFBM) of Hurst index H ∈ (1 2 , 1) and tempering parameter λ > 0 , by using the Wick product. The main tools are fractional calculus and Malliavin calculus. The Itô formula for this stochastic integral is established for the Itô type processes driven by TFBM. Based on this new Itô formula, we analyze the stability of stochastic differential equations driven by TFBM in the sense of p -th moment. A numerical example is given to illustrate our stability results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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18. Andriy Anatoliyovych Dorogovtsev (On His 60th Birthday).
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STOCHASTIC analysis , *STOCHASTIC integrals , *GAUSSIAN processes , *STOCHASTIC differential equations , *STOCHASTIC processes - Abstract
Andriy Anatoliyovych Dorogovtsev, a prominent Ukrainian mathematician, recently celebrated his 60th birthday. He is a Corresponding Member of the National Academy of Sciences of Ukraine, a doctor of physical and mathematical sciences, a professor, and the Head of the Department of the Theory of Random Processes at the Institute of Mathematics of the National Academy of Sciences of Ukraine. Dorogovtsev has made significant contributions to the field of mathematics, particularly in the areas of stochastic analysis, stochastic flows, and measure-valued processes. He is also known for his dedication to the popularization of mathematics and the training of young scientists. Dorogovtsev's colleagues and disciples admire his professionalism, passion for mathematics, and integrity in all aspects of life. [Extracted from the article]
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- 2024
- Full Text
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19. Stochastic dynamics of a nonlinear vibration energy harvester subjected to a combined parametric and external random excitation: The distinct cases of Itô and Stratonovich stochastic integration.
- Author
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Ramakrishnan, Subramanian and Singh, Aman Kumar
- Subjects
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RANDOM vibration , *STOCHASTIC differential equations , *ORNSTEIN-Uhlenbeck process , *STOCHASTIC integrals , *LYAPUNOV exponents , *STOCHASTIC systems , *WHITE noise , *COINTEGRATION - Abstract
The Stratonovich and Itô interpretations of a stochastic integral are mathematically consistent, distinct representations that yield contrasting response characteristics for stochastic dynamical systems subjected to multiplicative noise, such as parametric random excitation. The contrasting dynamics from the two interpretations currently remain unexplored in vibration energy harvester dynamics. We analytically investigate the dynamics of a generic piezoelectric, nonlinear vibration energy harvester simultaneously subjected to stochastic damping and external random excitation, focusing on the contrasting dynamics engendered by the two interpretations. Numerically solving the Stratonovich and Itô stochastic differential equations in the nonequilibrium regime of harvester dynamics, we find that the Stratonovich version yields significantly higher root mean square values of the harvester voltage output, for lower values of the mechanical damping coefficient. Furthermore, we find positive values for the leading Lyapunov exponent indicating instabilities in the harvester response unique to the Stratonovich interpretation. Additionally, comparing the results for the harvester electrical output between the cases of external excitation represented by the white noise and the Ornstein–Uhlenbeck noise processes, we find lower root mean square values of the voltage output in the latter case. Moreover, the results indicate that the averaged voltage output becomes progressively lower with increasing correlation time of the Ornstein–Uhlenbeck process. Studying the equilibrium dynamics by deriving Fokker–Planck equations for the response amplitude of the harvester using the harmonic balance method and stochastic averaging techniques, we solve for the stationary probability densities to find that the harvester is more likely to attain a well-defined equilibrium state under the Itô interpretation. In summary, the results contribute to the theoretical understanding of the fundamental contrast between the Stratonovich and Itô interpretations in vibration energy harvester dynamics and are expected to motivate advances in harvester design for various applications. • Vibration energy harvester studied under Itô and Stratonovich interpretations. • Stratonovich interpretation yields higher voltage for lower damping coefficient. • Lyapunov Exponent indicates instabilities under the Stratonovich interpretation. • Voltage output compared between white noise and Ornstein-Uhlenbeck excitation. • Voltage output compared between white noise and Ornstein-Uhlenbeck excitation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
20. Wasserstein distance estimates for jump-diffusion processes.
- Author
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Breton, Jean-Christophe and Privault, Nicolas
- Subjects
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STOCHASTIC differential equations , *STOCHASTIC integrals , *JUMP processes , *RANDOM measures , *DISTRIBUTION (Probability theory) - Abstract
We derive Wasserstein distance bounds between the probability distributions of a stochastic integral (Itô) process with jumps (X t) t ∈ [ 0 , T ] and a jump-diffusion process (X t ∗) t ∈ [ 0 , T ] . Our bounds are expressed using the stochastic characteristics of (X t) t ∈ [ 0 , T ] and the jump-diffusion coefficients of (X t ∗) t ∈ [ 0 , T ] evaluated in X t , and apply in particular to the case of different jump characteristics. Our approach uses stochastic calculus arguments and L p integrability results for the flow of stochastic differential equations with jumps, without relying on the Stein equation. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. Inequalities for fractional integral with the use of stochastic orderings.
- Author
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Epebinu, Abayomi Dennis and Szostok, Tomasz
- Subjects
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STOCHASTIC orders , *STOCHASTIC integrals , *FRACTIONAL integrals , *INTEGRAL inequalities - Abstract
In this paper, we show the connections of inequalities involving fractional integrals with Ohlin lemma and Levin-Stechkin theorem. First, we give a new proof of the fractional version of the inequality of Hermite Hadamard type and then we extend it in two directions. Thus we compare the fractional expression occurring in this inequality with the usual integral and we obtain stronger inequalities (one of them is related to Bullen inequality). • The use of stochastic orderings tools in the theory of inequalities for fractional integrals. • A new proof of the fractional version of the Hermite-Hadamard inequality. • Inequalities between the fractional integral and the regular one. • Refinements of Hermite-Hadamard inequality (in particular a fractional version of Bullen inequality). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
22. Stabilization of stochastic systems with sampled-state feedback controllers.
- Author
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Wang, Guoliang, Song, Siyong, and Zhang, Yande
- Subjects
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STOCHASTIC systems , *STATE feedback (Feedback control systems) , *STOCHASTIC integrals , *BROWNIAN motion , *CLOSED loop systems - Abstract
This paper explores the stabilization of continuous-time stochastic systems by a sampled-state feedback controller (SFC) placed in either drift or diffusion terms. Different from the traditionally state feedback controllers, the controller of a stochastic system in this paper is connected through a communication network, whose state needs to be sampled. Because of the controller state being sampled and Brownian motion existing simultaneously, it will be a challenge to ensure the stabilization of the closed-loop stochastic system. Particularly, it is very difficult to analyze the sampled-state error. To address this issue, an approach based on the exact integral solution to the stochastic error system is developed, in which some novel enlarging techniques are presented. Then, several stabilization conditions of stochastic systems based on the SFC added in the drift and diffusion terms respectively are established, whose upper sampling bound can be deduced and some of which are less conservative in terms of providing a larger sampling bound. Finally, the effectiveness and advantages of the proposed methods are illustrated with several numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Discrete Chebyshev polynomials for the numerical solution of stochastic fractional two-dimensional Sobolev equation.
- Author
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Heydari, M.H., Zhagharian, Sh., and Razzaghi, M.
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CHEBYSHEV polynomials , *ALGEBRAIC equations , *MATRICES (Mathematics) , *STOCHASTIC integrals , *STOCHASTIC matrices , *COLLOCATION methods - Abstract
In this work, the stochastic fractional two-dimensional Sobolev equation is introduced and a collocation method is proposed to solve it. The discrete Chebyshev polynomials are used as a proper family of basis functions to establish this collocation method. Some operational matrices related to conventional and stochastic integrals, as well as fractional and ordinary derivatives of these polynomials, are extracted and successfully used in making the expressed method. More precisely, by approximating the problem solution via a finite expansion of the expressed polynomials (where the expansion coefficients are unknown) and substituting it into the stochastic fractional problem, as well as by employing the above obtained matrices, a system of linear algebraic equations is obtained. Finally, the expansion coefficients and subsequently the solution of the original stochastic fractional problem are found by solving this system. The correctness of the established method is examined by solving some numerical examples. • The stochastic fractional two-dimensional Sobolev equation is introduced. • The orthonormal discrete Chebyshev polynomials (DCPs) are used to solve this equation. • An operational matrix of stochastic integral for the orthonormal DCPs is obtained. • Some operational matrices for derivatives of the orthonormal DCPs are extracted. • The accuracy of the proposed method is shown in some numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
24. Pricing formula for a Barrier call option based on stochastic delay differential equation.
- Author
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Kim, Kyong-Hui, Kim, Jong-Kuk, and Sin, Myong Guk
- Subjects
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STOCHASTIC differential equations , *OPTIONS (Finance) , *WIENER integrals , *DELAY differential equations , *PRICES , *STOCHASTIC integrals - Abstract
We derive new explicit pricing formulae for a type of Barrier call option, down and in call option when underlying asset price processes are represented by a stochastic delay differential equation (hereafter "SDDE"). We note the conditional normality of a stochastic integral with respect to a Wiener process to find the joint distribution of the stochastic integral and their minimum. On the basis of this result, we obtain pricing formulae for the Barrier call option which extends ones in the classical Black-Scholes models without delay. Finally, through Monte-Carlo simulations, we demonstrate that our theoretical prices for a Barrier option are correct. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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