A series approach to stochastic Volterra equations of convolution time

TL;DR

This paper investigates stochastic Volterra equations driven by series of Wiener processes, establishing conditions for strong solutions and analyzing the regularity of stochastic convolutions using a resolvent approach.

Contribution

It introduces a resolvent-based method to analyze stochastic Volterra equations of convolution type with series-driven noise, providing new existence and regularity results.

Findings

Sufficient conditions for strong solution existence.

Regularity results for stochastic convolutions.

Application of resolvent approach to convolution-type equations.

Abstract

In the paper stochastic Volterra equations with noise terms driven by series of independent scalar Wiener processes are considered. In our study we use the resolvent approach to the equations under consideration. We give sufficient condition for the existence of strong solution to the class of stochastic Volterra equations of convolution type. We provide regularity of stochastic convolution, as well.