Temporal and spatial regularity of solutions to stochastic Volterra equations of convolution type

TL;DR

This paper investigates the regularity properties of solutions to stochastic Volterra equations in Hilbert spaces, providing generalized conditions for their temporal and spatial regularity, extending known results for stochastic differential equations.

Contribution

It offers new sufficient conditions for the regularity of solutions to stochastic Volterra equations, broadening the understanding beyond classical stochastic differential equations.

Findings

Established conditions for temporal regularity

Established conditions for spatial regularity

Generalized known regularity results

Abstract

In the paper regularity of solutions to stochastic Volterra equations in a separable Hilbert space is studied. Sufficient conditions for the temporal and spatial regularity of stochastic convolutions corresponding to the equations under consideration are provided. The results obtained generalize some well-known regularity results for solutions to stochastic differential equations. The paper is a continuation of previous author's papers concerning stochastic Volterra equations.