The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations
Year: 2023
Author: Shanshan Xu, Lin Wang, Wenqiang Wang
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 4 : pp. 852–879
Abstract
In this paper, we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations (VFSDEs). We further constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the method. In particular, when the fractional order is no longer varying, the conclusions obtained are consistent with the relevant conclusions in the existing literature. Finally, the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2021-0222
Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 4 : pp. 852–879
Published online: 2023-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Variable-order Caputo fractional derivative Stochastic differential equations Euler-Maruyama method convergence multiplicative noise.