On an explicit representation of the solution of linear stochastic partial differential equations with delays

TL;DR

This paper derives a closed-form series solution for a class of linear stochastic partial differential equations with delays and non-autonomous inputs, advancing analytical methods in stochastic PDEs.

Contribution

It introduces an explicit infinite series representation for solutions of linear stochastic PDEs with delays, non-autonomous inputs, and stochastic terms.

Findings

Provides a closed-form infinite series solution

Extends analytical techniques to stochastic PDEs with delays

Enhances understanding of solution structures in stochastic PDEs

Abstract

Based on the analysis of a certain class of linear operators on a Banach space, we provide a closed form expression for the solutions of certain linear partial differential equations with non-autonomous input, time delays and stochastic terms, which takes the form of an infinite series expansion.