Large deviation principle for a stochastic heat equation with spatially correlated noise
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 equa...
| Autores: | , |
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| Tipo de documento: | artigo |
| Estado: | Versão publicada |
| Data de publicação: | 2003 |
| País: | España |
| Recursos: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositório: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/216681 |
| Acesso em linha: | https://hdl.handle.net/2445/216681 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Equacions diferencials parcials estocàstiques Equació de la calor Anàlisi estocàstica Stochastic partial differential equations Heat equation Stochastic analysis |
| Resumo: | 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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