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 - <p style="text-align: justify;">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.</p>