Approximation properties for solutions to Itô–Doob stochastic fractional differential equations with non-Lipschitz coefficients

Abstract

In this paper, we are concerned with the approximation theorem as an averaging principle for the solutions to stochastic fractional differential equations of Itô–Doob type with non-Lipschitz coefficients. The simplified systems will be investigated, and their solutions can be approximated to that of the original systems in the sense of mean square and probability, which constitute the approximation theorem. Two examples are presented with a numerical simulation to illustrate the obtained theory.