The Convergence of Euler-Maruyama Method of Nonlinear Variable-Order Fractional Stochastic Differential Equations (Advances in Applied Mathematics and Mechanics, 2023)
In this paper, we first prove the existence and uniqueness theorem of thesolution of nonlinear variable-order fractional stochastic differential equations (VFSDEs). We further constructe the Euler-Maruyama method to solve the equations andprove the convergence in mean and the strong convergence of the method. In particular, when the fractional order is no longer varying, the conclusions obtained areconsistent with the relevant conclusions in the existing literature. Finally, the numerical experiments at the end of the article verify the correctness of the theoretical resultsobtained.