Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise

In this article, we consider the Parabolic Anderson Model with constant initial condition, driven by a space-time homogeneous Gaussian noise, with general covariance function in time and spatial spectral measure satisfying Dalang's condition. First, we prove that the solution (in the Skorohod s...

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Detalles Bibliográficos
Autores: Balan, Raluca M., Quer i Sardanyons, Lluís|||0000-0001-8543-1595, Song, Jian
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:274597
Acceso en línea:https://ddd.uab.cat/record/274597
https://dx.doi.org/urn:doi:10.1007/s10473-019-0306-3
Access Level:acceso abierto
Palabra clave:60H07
60H15
Gaussian noise
Malliavin calculus
Stochastic partial differential equations
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spelling Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noiseBalan, Raluca M.Quer i Sardanyons, Lluís|||0000-0001-8543-1595Song, Jian60H0760H15Gaussian noiseMalliavin calculusStochastic partial differential equationsIn this article, we consider the Parabolic Anderson Model with constant initial condition, driven by a space-time homogeneous Gaussian noise, with general covariance function in time and spatial spectral measure satisfying Dalang's condition. First, we prove that the solution (in the Skorohod sense) exists and is continuous in Lp (Ω). Then, we show that the solution has a modification whose sample paths are Hölder continuous in space and time, under the minimal condition on the spatial spectral measure of the noise (which is the same as the condition encountered in the case of the white noise in time). This improves similar results which were obtained in [6, 10] under more restrictive conditions, and with sub-optimal exponents for Hölder continuity. 22019-01-0120192019-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/274597https://dx.doi.org/urn:doi:10.1007/s10473-019-0306-3reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2015-67802Popen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2745972026-06-06T12:50:31Z
dc.title.none.fl_str_mv Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
title Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
spellingShingle Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
Balan, Raluca M.
60H07
60H15
Gaussian noise
Malliavin calculus
Stochastic partial differential equations
title_short Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
title_full Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
title_fullStr Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
title_full_unstemmed Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
title_sort Hölder continuity for the Parabolic Anderson Model with space-time homogeneous Gaussian noise
dc.creator.none.fl_str_mv Balan, Raluca M.
Quer i Sardanyons, Lluís|||0000-0001-8543-1595
Song, Jian
author Balan, Raluca M.
author_facet Balan, Raluca M.
Quer i Sardanyons, Lluís|||0000-0001-8543-1595
Song, Jian
author_role author
author2 Quer i Sardanyons, Lluís|||0000-0001-8543-1595
Song, Jian
author2_role author
author
dc.subject.none.fl_str_mv 60H07
60H15
Gaussian noise
Malliavin calculus
Stochastic partial differential equations
topic 60H07
60H15
Gaussian noise
Malliavin calculus
Stochastic partial differential equations
description In this article, we consider the Parabolic Anderson Model with constant initial condition, driven by a space-time homogeneous Gaussian noise, with general covariance function in time and spatial spectral measure satisfying Dalang's condition. First, we prove that the solution (in the Skorohod sense) exists and is continuous in Lp (Ω). Then, we show that the solution has a modification whose sample paths are Hölder continuous in space and time, under the minimal condition on the spatial spectral measure of the noise (which is the same as the condition encountered in the case of the white noise in time). This improves similar results which were obtained in [6, 10] under more restrictive conditions, and with sub-optimal exponents for Hölder continuity.
publishDate 2019
dc.date.none.fl_str_mv 2
2019-01-01
2019
2019-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/274597
https://dx.doi.org/urn:doi:10.1007/s10473-019-0306-3
url https://ddd.uab.cat/record/274597
https://dx.doi.org/urn:doi:10.1007/s10473-019-0306-3
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2015-67802P
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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