Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications [PDF]
Entropy, 2018 In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions.
Xiao-Li Ding, Juan J. Nieto
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Maple for Stochastic Differential Equations [PDF]
, 2001 This paper introduces the MAPLE software package stochastic consisting of MAPLE routines for stochastic calculus and stochastic differential equations and for constructing basic numerical methods for specific stochastic differential equations, with simple examples illustrating the use of the routines.
Grüne, Lars +2 more
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Stability Analysis for a Class of Stochastic Differential Equations with Impulses
Mathematics, 2023 This paper is concerned with the problem of asymptotic stability for a class of stochastic differential equations with impulsive effects. A sufficient criterion on asymptotic stability is derived for such impulsive stochastic differential equations via ...
Mingli Xia +3 more
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Conservative Continuous-Stage Stochastic Runge–Kutta Methods for Stochastic Differential Equations
Fractal and Fractional, 2023 In this paper, we develop a new class of conservative continuous-stage stochastic Runge–Kutta methods for solving stochastic differential equations with a conserved quantity. The order conditions of the continuous-stage stochastic Runge–Kutta methods are
Xiuyan Li +3 more
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Equations Related to Stochastic Processes: Semigroup Approach and Fourier Transform
Современная математика: Фундаментальные направления, 2021 The work is devoted to integro-differential equations related to stochastic processes. We study the relationship between differential equations with random perturbations - stochastic differential equations (SDEs) - and deterministic equations for the ...
I. V. Melnikova +2 more
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Stochastic Runge–Kutta methods for multi-dimensional Itô stochastic differential algebraic equations
Results in Applied Mathematics, 2021 In this paper, we discuss the numerical solutions to index 1 stochastic differential algebraic equations. We introduce a new class of weak second-order stochastic Runge–Kutta methods for finding the numerical approximate solutions to multi-dimensional ...
Priya Nair, Anandaraman Rathinasamy
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Stochastic Differential Equations
Journal of Multivariate Analysis, 1974 AbstractWhen a system is acted upon by exterior disturbances, its time-development can often be described by a system of ordinary differential equations, provided that the disturbances are smooth functions. But for sound reasons physicists and engineers usually want the theory to apply when the noises belong to a larger class, including for example ...
M. Pinsky, I. I. Gihman, A. V. Skorohod
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An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations
Journal of Mathematics, 2021 In this paper, we want to establish an averaging principle for Mckean–Vlasov-type Caputo fractional stochastic differential equations with Brownian motion.
Weifeng Wang +3 more
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Optimal harvesting for a stochastic competition system with stage structure and distributed delay
Electronic Journal of Qualitative Theory of Differential Equations, 2021 A stochastic competition system with harvesting and distributed delay is investigated, which is described by stochastic differential equations with distributed delay.
Yue Zhang, Jing Zhang
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Caratheodory’s approximation for a type of Caputo fractional stochastic differential equations
Advances in Difference Equations, 2020 The Caratheodory approximation for a type of Caputo fractional stochastic differential equations is considered. As is well known, under the Lipschitz and linear growth conditions, the existence and uniqueness of solutions for some type of differential ...
Zhongkai Guo, Junhao Hu, Weifeng Wang
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