Asymptotic behaviour of the density in a parabolic SPDE

Consider the density of the solution $X(t, x)$ of a stochastic heat equation with small noise at a fixed $t \in[0, T], x \in[0,1]$. In this paper we study the asymptotics of this density as the noise vanishes. A kind of Taylor expansion in powers of the noise parameter is obtained. The coefficients...

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Autores: Kohatsu, Arturo, Márquez, David (Márquez Carreras), Sanz-Solé, Marta
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2001
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/216655
Acceso en línea:https://hdl.handle.net/2445/216655
Access Level:acceso abierto
Palabra clave:Grans desviacions
Càlcul de Malliavin
Equacions diferencials estocàstiques
Equacions diferencials parabòliques
Large deviations
Malliavin calculus
Stochastic differential equations
Parabolic differential equations
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spelling Asymptotic behaviour of the density in a parabolic SPDEKohatsu, ArturoMárquez, David (Márquez Carreras)Sanz-Solé, MartaGrans desviacionsCàlcul de MalliavinEquacions diferencials estocàstiquesEquacions diferencials parabòliquesLarge deviationsMalliavin calculusStochastic differential equationsParabolic differential equationsConsider the density of the solution $X(t, x)$ of a stochastic heat equation with small noise at a fixed $t \in[0, T], x \in[0,1]$. In this paper we study the asymptotics of this density as the noise vanishes. A kind of Taylor expansion in powers of the noise parameter is obtained. The coefficients and the residue of the expansion are explicitly calculated. In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximating process and the limit one is proved. Also a suitable iterative local integration by parts formula is developed.Springer Verlag2024202420012024info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion35 p.application/pdfapplication/pdfhttps://hdl.handle.net/2445/216655Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a:Journal of Theoretical Probability, 2001, vol. 14, num.2, p. 427-462(c) Springer Verlag, 2001info:eu-repo/semantics/openAccessoai:recercat.cat:2445/2166552026-05-29T05:05:01Z
dc.title.none.fl_str_mv Asymptotic behaviour of the density in a parabolic SPDE
title Asymptotic behaviour of the density in a parabolic SPDE
spellingShingle Asymptotic behaviour of the density in a parabolic SPDE
Kohatsu, Arturo
Grans desviacions
Càlcul de Malliavin
Equacions diferencials estocàstiques
Equacions diferencials parabòliques
Large deviations
Malliavin calculus
Stochastic differential equations
Parabolic differential equations
title_short Asymptotic behaviour of the density in a parabolic SPDE
title_full Asymptotic behaviour of the density in a parabolic SPDE
title_fullStr Asymptotic behaviour of the density in a parabolic SPDE
title_full_unstemmed Asymptotic behaviour of the density in a parabolic SPDE
title_sort Asymptotic behaviour of the density in a parabolic SPDE
dc.creator.none.fl_str_mv Kohatsu, Arturo
Márquez, David (Márquez Carreras)
Sanz-Solé, Marta
author Kohatsu, Arturo
author_facet Kohatsu, Arturo
Márquez, David (Márquez Carreras)
Sanz-Solé, Marta
author_role author
author2 Márquez, David (Márquez Carreras)
Sanz-Solé, Marta
author2_role author
author
dc.subject.none.fl_str_mv Grans desviacions
Càlcul de Malliavin
Equacions diferencials estocàstiques
Equacions diferencials parabòliques
Large deviations
Malliavin calculus
Stochastic differential equations
Parabolic differential equations
topic Grans desviacions
Càlcul de Malliavin
Equacions diferencials estocàstiques
Equacions diferencials parabòliques
Large deviations
Malliavin calculus
Stochastic differential equations
Parabolic differential equations
description Consider the density of the solution $X(t, x)$ of a stochastic heat equation with small noise at a fixed $t \in[0, T], x \in[0,1]$. In this paper we study the asymptotics of this density as the noise vanishes. A kind of Taylor expansion in powers of the noise parameter is obtained. The coefficients and the residue of the expansion are explicitly calculated. In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximating process and the limit one is proved. Also a suitable iterative local integration by parts formula is developed.
publishDate 2001
dc.date.none.fl_str_mv 2001
2024
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/216655
url https://hdl.handle.net/2445/216655
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a:
Journal of Theoretical Probability, 2001, vol. 14, num.2, p. 427-462
dc.rights.none.fl_str_mv (c) Springer Verlag, 2001
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Springer Verlag, 2001
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 35 p.
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer Verlag
publisher.none.fl_str_mv Springer Verlag
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.812429

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