Large deviations for a fractional stochastic heat equation in spatial dimension ℝd driven by a spatially correlated noise

Abstract

In this paper we study the Large Deviations Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space [Formula: see text], with arbitrary dimension [Formula: see text], under random influence which is a Gaussian noise, white in time and correlated in space. The differential operator is a fractional derivative operator. We prove a Large deviations principle for our equation, using a weak convergence approach based on a variational representation of functionals of infinite-dimensional Brownian motion. This approach reduces the proof of LDP to establishing basic qualitative properties for controlled analogues of the original stochastic system.