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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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