Large deviations for stochastic heat equations with memory driven by Levy-type noise

TL;DR

This paper proves the existence and uniqueness of solutions for a stochastic heat equation with memory driven by Levy-type noise, and establishes a large deviation principle using the weak convergence approach.

Contribution

It introduces a novel analysis of large deviations for heat equations with memory under Levy noise, employing the weak convergence method.

Findings

Existence and uniqueness of solutions established.

Large deviation principle proven for the solutions.

Application of weak convergence approach to Levy-driven equations.

Abstract

For a heat equation with memory driven by a L\'evy-type noise we establish the existence of a unique solution. The main part of the article focuses on the Freidlin-Wentzell large deviation principle of the solutions of heat equation with memory driven by a L\'evy-type noise. For this purpose, we exploit the recently introduced weak convergence approach.