Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/216681
Title: Large deviation principle for a stochastic heat equation with spatially correlated noise
Author: Márquez, David (Márquez Carreras)
Sarrà, Mònica
Keywords: Equacions diferencials parcials estocàstiques
Equació de la calor
Anàlisi estocàstica
Stochastic partial differential equations
Heat equation
Stochastic analysis
Issue Date: 2003
Publisher: Institute of Mathematical Statistics (IMS) and the Bernoulli Society for Mathematical Statistics and Probability
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.
Note: Reproducció del document publicat a: https://doi.org/10.1214/EJP.v8-146
It is part of: Electronic Journal of Probability, 2003, vol. 8, num.12, p. 1-39
URI: https://hdl.handle.net/2445/216681
Related resource: https://doi.org/10.1214/EJP.v8-146
ISSN: 1083-6489
Appears in Collections:Articles publicats en revistes (Matemàtiques i Informàtica)

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