The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations

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.

Author Details

Shanshan Xu

Lin Wang

Wenqiang Wang