Strong convergence of the Euler-Maruyama method for the generalized stochastic Volterra integral equations driven by L\'evy noise

Abstract

In this paper, the theoretical and numerical analysis of the stochastic Volterra integro-differential equations (SVIEs) driven by L\'evy noise are considered. We investigate the existence, uniqueness, boundedness and H\"older continuity of the analytic solutions for SVIDEs driven by L\'evy noise. The Euler-Maruyama method for SVIEs driven by L\'evy noise is proposed. The boundedness of the numerical solution is proved, and the strong convergence order is obtained. Some numerical examples are given to support the theoretical results.