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

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.