Stochastic shell models driven by a multiplicative fractional Brownian-motion

We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter H∈(1/2,1), and contains a non--trivial coefficient in front of the noise which satisfies special regularity conditions....

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Authors: Bessaih, Hakima, Garrido Atienza, María José, Schmalfuss, Björn
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2016
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/43248
Online Access:http://hdl.handle.net/11441/43248
https://doi.org/10.1016/j.physd.2016.01.008
Access Level:Open access
Keyword:Stochastic PDEs
Fractional Brownian-motion
Pathwise solutions
Fractional calculus
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spelling Stochastic shell models driven by a multiplicative fractional Brownian-motionBessaih, HakimaGarrido Atienza, María JoséSchmalfuss, BjörnStochastic PDEsFractional Brownian-motionPathwise solutionsFractional calculusWe prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter H∈(1/2,1), and contains a non--trivial coefficient in front of the noise which satisfies special regularity conditions. The appearing stochastic integrals are defined in a fractional sense. First, we prove the existence and uniqueness of variational solutions to approximating equations driven by piecewise linear continuous noise, for which we are able to derive important uniform estimates in some functional spaces. Then, thanks to a compactness argument and these estimates, we prove that these variational solutions converge to a limit solution, which turns out to be the unique pathwise mild solution associated to the shell--model with fractional noise as driving process.Simons FoundationNational Science FoundationElsevierEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas DiferencialesSimons FoundationNational Science Foundation (NSF). United States2016info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/43248https://doi.org/10.1016/j.physd.2016.01.008reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésPhysica D: Nonlinear Phenomena, 320, 38-56.2833081416689http://dx.doi.org/10.1016/j.physd.2016.01.008info:eu-repo/semantics/openAccessoai:idus.us.es:11441/432482026-06-17T12:51:07Z
dc.title.none.fl_str_mv Stochastic shell models driven by a multiplicative fractional Brownian-motion
title Stochastic shell models driven by a multiplicative fractional Brownian-motion
spellingShingle Stochastic shell models driven by a multiplicative fractional Brownian-motion
Bessaih, Hakima
Stochastic PDEs
Fractional Brownian-motion
Pathwise solutions
Fractional calculus
title_short Stochastic shell models driven by a multiplicative fractional Brownian-motion
title_full Stochastic shell models driven by a multiplicative fractional Brownian-motion
title_fullStr Stochastic shell models driven by a multiplicative fractional Brownian-motion
title_full_unstemmed Stochastic shell models driven by a multiplicative fractional Brownian-motion
title_sort Stochastic shell models driven by a multiplicative fractional Brownian-motion
dc.creator.none.fl_str_mv Bessaih, Hakima
Garrido Atienza, María José
Schmalfuss, Björn
author Bessaih, Hakima
author_facet Bessaih, Hakima
Garrido Atienza, María José
Schmalfuss, Björn
author_role author
author2 Garrido Atienza, María José
Schmalfuss, Björn
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
Simons Foundation
National Science Foundation (NSF). United States
dc.subject.none.fl_str_mv Stochastic PDEs
Fractional Brownian-motion
Pathwise solutions
Fractional calculus
topic Stochastic PDEs
Fractional Brownian-motion
Pathwise solutions
Fractional calculus
description We prove existence and uniqueness of the solution of a stochastic shell--model. The equation is driven by an infinite dimensional fractional Brownian--motion with Hurst--parameter H∈(1/2,1), and contains a non--trivial coefficient in front of the noise which satisfies special regularity conditions. The appearing stochastic integrals are defined in a fractional sense. First, we prove the existence and uniqueness of variational solutions to approximating equations driven by piecewise linear continuous noise, for which we are able to derive important uniform estimates in some functional spaces. Then, thanks to a compactness argument and these estimates, we prove that these variational solutions converge to a limit solution, which turns out to be the unique pathwise mild solution associated to the shell--model with fractional noise as driving process.
publishDate 2016
dc.date.none.fl_str_mv 2016
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/43248
https://doi.org/10.1016/j.physd.2016.01.008
url http://hdl.handle.net/11441/43248
https://doi.org/10.1016/j.physd.2016.01.008
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Physica D: Nonlinear Phenomena, 320, 38-56.
283308
1416689
http://dx.doi.org/10.1016/j.physd.2016.01.008
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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