Estimates for the volume variation of compact submanifolds driven by a stochastic flow
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1080/14689367.2022.2078686 http://hdl.handle.net/11449/240240 |
Resumo: | Consider a compact submanifold N without the boundary of a Riemannian manifold M, and a stochastic flow (Formula presented.) associated with a stochastic differential equation. Let (Formula presented.) be the random compact submanifold obtained by the action of the stochastic flow. In this work, we present an Itô formula for the volume of the random variable (Formula presented.) and, as a main result, we obtain estimates for its average growth assuming that Ricci curvature is bounded. We first analyse the particular case where the submanifolds are closed curves, thus obtaining estimates for the arc length, and then we study the volume variation of compact submanifolds of dimensions greater than or equal to 2. In addition, we apply our results to the special case where the vector fields of stochastic differential equation are conformal Killing. |
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Repositório Institucional da UNESP |
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Estimates for the volume variation of compact submanifolds driven by a stochastic flow58J6560H1060J60compact submanifoldFréchet manifoldstochastic flowVolume growth estimateConsider a compact submanifold N without the boundary of a Riemannian manifold M, and a stochastic flow (Formula presented.) associated with a stochastic differential equation. Let (Formula presented.) be the random compact submanifold obtained by the action of the stochastic flow. In this work, we present an Itô formula for the volume of the random variable (Formula presented.) and, as a main result, we obtain estimates for its average growth assuming that Ricci curvature is bounded. We first analyse the particular case where the submanifolds are closed curves, thus obtaining estimates for the arc length, and then we study the volume variation of compact submanifolds of dimensions greater than or equal to 2. In addition, we apply our results to the special case where the vector fields of stochastic differential equation are conformal Killing.Universidade Estadual de CampinasUniversidade Estadual Paulista UNESPUniversidade Estadual Paulista UNESPUniversidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (UNESP)Ledesma, Diego SebastianAnaya, Robert Andres GaleanoSilva, Fabiano Borges da [UNESP]2023-03-01T20:07:55Z2023-03-01T20:07:55Z2022-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1080/14689367.2022.2078686Dynamical Systems.1468-93751468-9367http://hdl.handle.net/11449/24024010.1080/14689367.2022.20786862-s2.0-85131838951Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengDynamical Systemsinfo:eu-repo/semantics/openAccess2023-03-01T20:07:55Zoai:repositorio.unesp.br:11449/240240Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T19:38:22.526678Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Estimates for the volume variation of compact submanifolds driven by a stochastic flow |
title |
Estimates for the volume variation of compact submanifolds driven by a stochastic flow |
spellingShingle |
Estimates for the volume variation of compact submanifolds driven by a stochastic flow Ledesma, Diego Sebastian 58J65 60H10 60J60 compact submanifold Fréchet manifold stochastic flow Volume growth estimate |
title_short |
Estimates for the volume variation of compact submanifolds driven by a stochastic flow |
title_full |
Estimates for the volume variation of compact submanifolds driven by a stochastic flow |
title_fullStr |
Estimates for the volume variation of compact submanifolds driven by a stochastic flow |
title_full_unstemmed |
Estimates for the volume variation of compact submanifolds driven by a stochastic flow |
title_sort |
Estimates for the volume variation of compact submanifolds driven by a stochastic flow |
author |
Ledesma, Diego Sebastian |
author_facet |
Ledesma, Diego Sebastian Anaya, Robert Andres Galeano Silva, Fabiano Borges da [UNESP] |
author_role |
author |
author2 |
Anaya, Robert Andres Galeano Silva, Fabiano Borges da [UNESP] |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual de Campinas (UNICAMP) Universidade Estadual Paulista (UNESP) |
dc.contributor.author.fl_str_mv |
Ledesma, Diego Sebastian Anaya, Robert Andres Galeano Silva, Fabiano Borges da [UNESP] |
dc.subject.por.fl_str_mv |
58J65 60H10 60J60 compact submanifold Fréchet manifold stochastic flow Volume growth estimate |
topic |
58J65 60H10 60J60 compact submanifold Fréchet manifold stochastic flow Volume growth estimate |
description |
Consider a compact submanifold N without the boundary of a Riemannian manifold M, and a stochastic flow (Formula presented.) associated with a stochastic differential equation. Let (Formula presented.) be the random compact submanifold obtained by the action of the stochastic flow. In this work, we present an Itô formula for the volume of the random variable (Formula presented.) and, as a main result, we obtain estimates for its average growth assuming that Ricci curvature is bounded. We first analyse the particular case where the submanifolds are closed curves, thus obtaining estimates for the arc length, and then we study the volume variation of compact submanifolds of dimensions greater than or equal to 2. In addition, we apply our results to the special case where the vector fields of stochastic differential equation are conformal Killing. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-01-01 2023-03-01T20:07:55Z 2023-03-01T20:07:55Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1080/14689367.2022.2078686 Dynamical Systems. 1468-9375 1468-9367 http://hdl.handle.net/11449/240240 10.1080/14689367.2022.2078686 2-s2.0-85131838951 |
url |
http://dx.doi.org/10.1080/14689367.2022.2078686 http://hdl.handle.net/11449/240240 |
identifier_str_mv |
Dynamical Systems. 1468-9375 1468-9367 10.1080/14689367.2022.2078686 2-s2.0-85131838951 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Dynamical Systems |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129099392090112 |