Properties of convolutions arising in stochastic Volterra equations

Abstract

The aim of this note is to provide some results for stochastic convolutions corresponding to stochastic Volterra equations in separable Hilbert space. We study convolution of the form $W^Ψ(t):=\int_0^t S(t-τ)Ψ(τ)dW(τ)$, $t\geq 0$, where $S(t), t\geq 0$, is so-called {\em resolvent} for Volterra equation considered,$Ψ$ is an appropriate process and $W$ is a cylindrical Wiener process.