Decomposition of stochastic flow and an averaging principle for slow perturbations
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1080/14689367.2020.1769031 http://hdl.handle.net/11449/199006 |
Resumo: | In this work we use the stochastic flow decomposition technique to get components that represent the dynamics of the slow and fast motion of a stochastic differential equation with a random perturbation. Assuming a Lipschitz condition for vector fields and an average principle we get an approximation for the slow motion. To obtain the estimate for the rate of convergence we use a distance function which is defined in terms of the height functions associated to an isometric embedding of the manifold into the Euclidean space. This metric is topologically equivalent to the Riemannian distance given by the infimum of the lengths of all admissible curves between two points and works well with stochastic calculation tools. Finally, we get an estimate for the approximation between the solution of perturbed system and the original process provided by the unperturbed. |
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Decomposition of stochastic flow and an averaging principle for slow perturbationsAveraging principledecomposition of stochastic flowdiffusionslow perturbationsIn this work we use the stochastic flow decomposition technique to get components that represent the dynamics of the slow and fast motion of a stochastic differential equation with a random perturbation. Assuming a Lipschitz condition for vector fields and an average principle we get an approximation for the slow motion. To obtain the estimate for the rate of convergence we use a distance function which is defined in terms of the height functions associated to an isometric embedding of the manifold into the Euclidean space. This metric is topologically equivalent to the Riemannian distance given by the infimum of the lengths of all admissible curves between two points and works well with stochastic calculation tools. Finally, we get an estimate for the approximation between the solution of perturbed system and the original process provided by the unperturbed.Universidade Estadual de CampinasUniversidade Estadual Paulista UNESPUniversidade Estadual Paulista UNESPUniversidade Estadual de Campinas (UNICAMP)Universidade Estadual Paulista (Unesp)Ledesma, Diego SebastianBorges da Silva, Fabiano [UNESP]2020-12-12T01:28:09Z2020-12-12T01:28:09Z2020-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1080/14689367.2020.1769031Dynamical Systems.1468-93751468-9367http://hdl.handle.net/11449/19900610.1080/14689367.2020.17690312-s2.0-85086665466Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengDynamical Systemsinfo:eu-repo/semantics/openAccess2021-10-22T22:17:26Zoai:repositorio.unesp.br:11449/199006Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:10:48.759398Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Decomposition of stochastic flow and an averaging principle for slow perturbations |
title |
Decomposition of stochastic flow and an averaging principle for slow perturbations |
spellingShingle |
Decomposition of stochastic flow and an averaging principle for slow perturbations Ledesma, Diego Sebastian Averaging principle decomposition of stochastic flow diffusion slow perturbations |
title_short |
Decomposition of stochastic flow and an averaging principle for slow perturbations |
title_full |
Decomposition of stochastic flow and an averaging principle for slow perturbations |
title_fullStr |
Decomposition of stochastic flow and an averaging principle for slow perturbations |
title_full_unstemmed |
Decomposition of stochastic flow and an averaging principle for slow perturbations |
title_sort |
Decomposition of stochastic flow and an averaging principle for slow perturbations |
author |
Ledesma, Diego Sebastian |
author_facet |
Ledesma, Diego Sebastian Borges da Silva, Fabiano [UNESP] |
author_role |
author |
author2 |
Borges da Silva, Fabiano [UNESP] |
author2_role |
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 Borges da Silva, Fabiano [UNESP] |
dc.subject.por.fl_str_mv |
Averaging principle decomposition of stochastic flow diffusion slow perturbations |
topic |
Averaging principle decomposition of stochastic flow diffusion slow perturbations |
description |
In this work we use the stochastic flow decomposition technique to get components that represent the dynamics of the slow and fast motion of a stochastic differential equation with a random perturbation. Assuming a Lipschitz condition for vector fields and an average principle we get an approximation for the slow motion. To obtain the estimate for the rate of convergence we use a distance function which is defined in terms of the height functions associated to an isometric embedding of the manifold into the Euclidean space. This metric is topologically equivalent to the Riemannian distance given by the infimum of the lengths of all admissible curves between two points and works well with stochastic calculation tools. Finally, we get an estimate for the approximation between the solution of perturbed system and the original process provided by the unperturbed. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-12-12T01:28:09Z 2020-12-12T01:28:09Z 2020-01-01 |
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/10.1080/14689367.2020.1769031 Dynamical Systems. 1468-9375 1468-9367 http://hdl.handle.net/11449/199006 10.1080/14689367.2020.1769031 2-s2.0-85086665466 |
url |
http://dx.doi.org/10.1080/14689367.2020.1769031 http://hdl.handle.net/11449/199006 |
identifier_str_mv |
Dynamical Systems. 1468-9375 1468-9367 10.1080/14689367.2020.1769031 2-s2.0-85086665466 |
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_ |
1808128614762283008 |