Wong-Zakai Approximations for Stochastic Volterra Equations

Abstract

In this paper, we shall prove a Wong-Zakai approximation for stochastic Volterra equations under appropriate assumptions. We may apply it to a class of stochastic differential equations with the kernel of fractional Brownian motion with Hurst parameter $H ∈ (1/2, 1)$ and subfractional Brownian motion with Hurst parameter $H ∈ (1/2, 1).$ As far as we know, this is the first result on stochastic Volterra equations in this topic.