Large deviations for a fractional stochastic heat equation in spatial dimension ${\mathbb{R}}^d$ driven by a spatially correlated noise

Abstract

In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space ${\mathbb{R}}^d$, with arbitrary dimension $d\ge 1$, 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.

This paper has been accepted for publication in Stochastics & Dynamics. This reprint differs from the original in pagination and typographic detail. arXiv admin note: text overlap with arXiv:1309.1935 by other authors

References in corpus (2)

• Large deviations for infinite dimensional stochastic dynamical systems
• Large deviations for the Boussinesq Equations under Random Influences