Regularity of solutions to stochastic Volterra equations of convolution type

Abstract

In this paper we consider two classes of linear Volterra equations: of convolution type on ℝ+ and integro-differential with infinite delay on d-dimensional torus, both driven by spatially homogeneous Wiener process. First, we study the existence of solutions to these equations in the space of tempered distributions and then derive conditions under which the solutions take values in Sobolev spaces. We give necessary and sufficient conditions providing regularity of solutions to equations considered. The harmonic analysis techniques and stochastic integration in function spaces are used. The paper is a short review of regularity results for stochastic Volterra equations of convolution type.