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 H"older continuity for
the solution of the stochastic heat
equation.
Secondly, we check that our Gaussian process satisfies a
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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