Convergence of the θ-Euler-Maruyama method for a class of stochastic Volterra integro-differential equations

Abstract

This paper addresses the convergence analysis of the θ-Euler-Maruyama method for a class of stochastic Volterra integro-differential equations (SVIDEs). At first, we discuss the existence, uniqueness, boundedness and H¨older continuity of the theoretical solution. Subsequently, the strong convergence order of the θ-Euler-Maruyama approach for SVIDEs is shown. Finally, we provided numerical examples to illustrate the theoretical results.

Keywords

• Stochastic Volterra integro-differential equations, Θ-Euler-Maruyama method, strong convergence, H¨older continuity.