Theoretical and numerical analysis of a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients

Abstract

In this paper, we consider the theoretical and numerical analysis of a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients. The existence, uniqueness and pth moment boundedness of the analytic solutions are investigated. Euler method is shown to be divergent in the strong mean square sense for super linear growth coefficients, so the truncated Euler-Maruyama method is presented and its moment boundedness and Lq-convergence are shown. Moreover, its pth moment boundedness and Lq-convergence (q∈[2,p) and p is a parameter in Khasminskii-type condition) rate are given under Local Lipschitz condition and Khasminskii-type condition. The theoretical results are illustrated by some numerical examples.