Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs

We consider a Lévy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a semilin...

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Autores: Bardina, Xavier|||0000-0003-1803-3401, Márquez, Juan Pablo, Quer i Sardanyons, Lluís|||0000-0001-8543-1595
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:274609
Acesso em linha:https://ddd.uab.cat/record/274609
https://dx.doi.org/urn:doi:10.1016/j.spa.2020.04.006
Access Level:acceso abierto
Palavra-chave:Brownian sheet
Lévy sheet
Stochastic heat equation
Weak approximation
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spelling Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEsBardina, Xavier|||0000-0003-1803-3401Márquez, Juan PabloQuer i Sardanyons, Lluís|||0000-0001-8543-1595Brownian sheetLévy sheetStochastic heat equationWeak approximationWe consider a Lévy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a semilinear one-dimensional stochastic heat equation driven by the space-time white noise.Universitat Autònoma de Barcelona. Departament de Matemàtiques 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/274609https://dx.doi.org/urn:doi:10.1016/j.spa.2020.04.006reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-097848-B-I00open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2746092026-06-06T12:50:31Z
dc.title.none.fl_str_mv Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs
title Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs
spellingShingle Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs
Bardina, Xavier|||0000-0003-1803-3401
Brownian sheet
Lévy sheet
Stochastic heat equation
Weak approximation
title_short Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs
title_full Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs
title_fullStr Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs
title_full_unstemmed Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs
title_sort Weak approximation of the complex Brownian sheet from a Lévy sheet and applications to SPDEs
dc.creator.none.fl_str_mv Bardina, Xavier|||0000-0003-1803-3401
Márquez, Juan Pablo
Quer i Sardanyons, Lluís|||0000-0001-8543-1595
author Bardina, Xavier|||0000-0003-1803-3401
author_facet Bardina, Xavier|||0000-0003-1803-3401
Márquez, Juan Pablo
Quer i Sardanyons, Lluís|||0000-0001-8543-1595
author_role author
author2 Márquez, Juan Pablo
Quer i Sardanyons, Lluís|||0000-0001-8543-1595
author2_role author
author
dc.contributor.none.fl_str_mv Universitat Autònoma de Barcelona. Departament de Matemàtiques
dc.subject.none.fl_str_mv Brownian sheet
Lévy sheet
Stochastic heat equation
Weak approximation
topic Brownian sheet
Lévy sheet
Stochastic heat equation
Weak approximation
description We consider a Lévy process in the plane and we use it to construct a family of complex-valued random fields that we show to converge in law, in the space of continuous functions, to a complex Brownian sheet. We apply this result to obtain weak approximations of the random field solution to a semilinear one-dimensional stochastic heat equation driven by the space-time white noise.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
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/274609
https://dx.doi.org/urn:doi:10.1016/j.spa.2020.04.006
url https://ddd.uab.cat/record/274609
https://dx.doi.org/urn:doi:10.1016/j.spa.2020.04.006
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PGC2018-097848-B-I00
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
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://creativecommons.org/licenses/by-nc-nd/4.0/
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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