Analysis and Numerical Approximation for a Nonlinear Hidden-Memory Variable-Order Fractional Stochastic Differential Equation

Abstract

We prove the well-posedness of a nonlinear hidden-memory variable-order fractional stochastic differential equation driven by a multiplicative white noise, in which the hidden-memory type variable order describes the memory of a fractional order. We then present a Euler-Maruyama scheme for the proposed model and prove its strong convergence rate. Numerical experiments are performed to substantiate the theoretical results.