Moderate deviations for a fractional stochastic heat equation with spatially correlated noise

TL;DR

This paper establishes a Moderate Deviation Principle for a fractional stochastic heat equation driven by spatially correlated Gaussian noise, using the weak convergence method to analyze deviations in an infinite spatial domain.

Contribution

It introduces the Moderate Deviation Principle for a fractional stochastic heat equation with spatially correlated noise, extending existing results to fractional derivatives and unbounded domains.

Findings

Established the Moderate Deviation Principle for the equation

Applied weak convergence method effectively in this context

Extended analysis to fractional derivatives and spatially correlated noise

Abstract

In this paper, we study the Moderate Deviation Principle for a perturbed stochastic heat equation in the whole space $\rr^d, d\ge1$. This equation is driven by a Gaussian noise, white in time and correlated in space, and the differential operator is a fractional derivative operator. The weak convergence method plays an important role.