Large Deviation Principle for a Stochastic Heat Equation With Spatially Correlated Noise

David Marquez-Carreras (Universitat de Barcelona)
Monica Sarra (Universitat de Barcelona)

Abstract


In this paper we prove a large deviation principle (LDP) for a perturbed stochastic heat equation defined on $[0,T]\times [0,1]^d$. This equation is driven by a Gaussian noise, white in time and correlated in space. Firstly, we show the Holder continuity for the solution of the stochastic heat equation. Secondly, we check that our Gaussian process satisfies an LDP and some requirements on the skeleton of the solution. Finally, we prove the called Freidlin-Wentzell inequality. In order to obtain all these results we need precise estimates of the fundamental solution of this equation.

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Pages: 1-39

Publication Date: July 18, 2003

DOI: 10.1214/EJP.v8-146

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