Split-step ϑ integrator for generalized stochastic Volterra integro-differential equations

Abstract

This study investigates the theoretical analysis and numerical approximation of generalized stochastic Volterra integro-differential equations. First, we examine the existence, uniqueness, boundedness and Hölder continuity of the exact solutions for generalized SVIDEs. To numerically solve, the split-step $\vartheta$ integrator is proposed. We then demonstrate the boundedness of the numerical solution. Further, it has been shown that the scheme is strongly convergent with order half. Numerical experiments are carried out to support our findings.