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Volume 15, Issue 4
The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations

Shanshan Xu, Lin Wang & Wenqiang Wang

Adv. Appl. Math. Mech., 15 (2023), pp. 852-879.

Published online: 2023-04

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  • 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.

  • AMS Subject Headings

34A12, 65C30, 90B36

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COPYRIGHT: © Global Science Press

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@Article{AAMM-15-852, author = {Xu , ShanshanWang , Lin and Wang , Wenqiang}, title = {The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2023}, volume = {15}, number = {4}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/ 10.4208/aamm.OA-2021-0222}, url = {http://global-sci.org/intro/article_detail/aamm/21590.html} }
TY - JOUR T1 - The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations AU - Xu , Shanshan AU - Wang , Lin AU - Wang , Wenqiang JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 852 EP - 879 PY - 2023 DA - 2023/04 SN - 15 DO - http://doi.org/ 10.4208/aamm.OA-2021-0222 UR - https://global-sci.org/intro/article_detail/aamm/21590.html KW - Variable-order Caputo fractional derivative, Stochastic differential equations, Euler-Maruyama method, convergence, multiplicative noise. AB -

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.

Shanshan Xu, Lin Wang & Wenqiang Wang. (2023). The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations. Advances in Applied Mathematics and Mechanics. 15 (4). 852-879. doi: 10.4208/aamm.OA-2021-0222
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