Strong convergence of the Euler-Maruyama method for the generalized stochastic Volterra integral equations driven by Lévy Noise


Wei Zhang, Rui Li




In this paper, the theoretical and numerical analysis of the stochastic Volterra integral equations (SVIEs) driven by Lévy noise are considered. We investigate the existence, uniqueness, boundedness and H ¨ older continuity of the analytic solutions for SVIEs driven by Lévy noise. The Euler-Maruyama method for SVIEs driven by Lévy 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.