A sharp error estimate of Euler‐Maruyama method for stochastic Volterra integral equations

Abstract

In this paper, the Euler-Maruyama method is used to solve a class of nonlinear stochastic Volterra integral equations (SVIEs), which can be derived from stochastic fractional substantial integro-differential equations (SFSIDEs). The existence and uniqueness of the solution are proved for the nonlinear SVIEs ] , respectively, is established for the nonlinear SVIEs, which can be revised as supplemented theory results of our recent work (J Comput Appl Math 356 (2019) 377-390). In particular, it also closes a gap that was left on the convergence analysis in (J Comput Appl Math 317 (2017) 447-457). Finally, numerical experiments are given to illustrate the effectiveness of the presented method.