Asymptotic separation for stochastic Volterra integral equations with doubly singular kernels

Abstract

In this paper, we study the exact asymptotic separation rate of two distinct solutions of doubly singular stochastic Volterra integral equations (SVIEs) with two different initial values. The main tool is the Gronwall inequality with doubly singular kernel. For a special linear singular SVIEs, we obtain a bound for the leading coefficient of the asymptotic separation rate for the two distinct solutions which reveals that our asymptotic results are sharp.