Function-valued stochastic convolutions arising in integrodifferential equations

TL;DR

This paper investigates stochastic convolutions linked to fundamental solutions of integrodifferential equations that bridge heat and wave equations, establishing conditions for their existence based on noise covariance kernels.

Contribution

It provides new sufficient conditions for the existence of function-valued stochastic convolutions in the context of integrodifferential equations.

Findings

Established criteria for convolution existence based on covariance kernels

Connected stochastic convolutions with heat and wave equation interpolations

Enhanced understanding of noise effects in integrodifferential equations

Abstract

We study stochastic convolutions providing by fundamental solutions of a class of integrodifferential equations which interpolate the heat and the wave equations. We give sufficient condition for the existence of function--valued convolutions in terms of the covariance kernel of a noise given by spatially homogeneous Wiener process.