Theoretical and numerical analysis of the Euler–Maruyama method for generalized stochastic Volterra integro-differential equations

Abstract In this paper, we concern with the theoretical and numerical analysis of the generalized stochastic Volterra integro-differential equations (SVIDEs). The existence, uniqueness, boundedness and Holder continuity of the analytic solutions for generalized SVIDEs are investigated. The Euler–Maruyama method for generalized SVIDEs is presented. The boundedness of the numerical solution is proved, and the strong convergence order is obtained. The theoretical results are illustrated by some numerical examples.