Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay

摘要

This paper is mainly concerned with the strong convergence analysis of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations (SVIEs) with constant delay. The solvability and the boundedness of the numerical solution are established. It is proved that the strong convergence order of the semi-implicit Euler method is 0.5 under Lipschitz conditions. Moreover, the strong superconvergence order is 1.0 if further, the kernel σ of the stochastic term satisfies σ(0)=σ(τ)=0. The theoretical results are illustrated by extensive numerical examples.