Poincaré recurrence times in stochastic mixing processes
Autor(a) principal: | |
---|---|
Data de Publicação: | 2022 |
Tipo de documento: | Tese |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/15733 |
Resumo: | In the context of the discrete-time stochastic processes, this thesis presents new results on Poincaré recurrence theory. After a complete review of recent results, we present a new theorem on the exponential approximations for hitting and return times distributions. We show that the scaling parameter of the approximate distribution, called "potential well", brings fundamental informations about the structure of the target set. Moreover, we show that the asymptotic properties of the potential well influences several aspects of the recurrence times, such as limiting distributions and moments. Finally, we apply our results to obtain the waiting time spectrum as a function of the Rényi entropy for classes of processes not covered by previous works. |
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Amorim, Vitor Gustavo deGallo, Alexsandro Giacomo Grimberthttp://lattes.cnpq.br/4037274656833325Abadi, Miguel Nataliohttp://lattes.cnpq.br/8422115514014109http://lattes.cnpq.br/5021711316846807f973b4f2-b626-4e5f-be42-d94bcd15c1992022-03-23T13:40:50Z2022-03-23T13:40:50Z2022-02-17AMORIM, Vitor Gustavo de. Poincaré recurrence times in stochastic mixing processes. 2022. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/15733.https://repositorio.ufscar.br/handle/ufscar/15733In the context of the discrete-time stochastic processes, this thesis presents new results on Poincaré recurrence theory. After a complete review of recent results, we present a new theorem on the exponential approximations for hitting and return times distributions. We show that the scaling parameter of the approximate distribution, called "potential well", brings fundamental informations about the structure of the target set. Moreover, we show that the asymptotic properties of the potential well influences several aspects of the recurrence times, such as limiting distributions and moments. Finally, we apply our results to obtain the waiting time spectrum as a function of the Rényi entropy for classes of processes not covered by previous works.Esta tese apresenta novos resultados na teoria de recorrência de Poincaré, no contexto de processos estocásticos em tempo discreto. Após uma revisão completa de resultados recentes, apresentamos um novo teorema sobre aproximação exponencial para distribuições de tempos de entrada e retorno. Mostramos que o parâmetro de escala da distribuição aproximada, chamado "poço de potencial", traz ao teorema de aproximação informações fundamentais sobre a estrutura do conjunto alvo. Além disso, mostramos que as propriedades assintóticas do poço de potencial influenciam vários aspectos dos tempos de recorrência, como as distribuições limite e seus momentos. Por fim, aplicamos nossos resultados para obter o espectro do tempo de espera como função da entropia de Rényi para classes de processos não cobertas por trabalhos anteriores.Não recebi financiamentoengUniversidade Federal de São CarlosCâmpus São CarlosPrograma Interinstitucional de Pós-Graduação em Estatística - PIPGEsUFSCarAttribution-NonCommercial-NoDerivs 3.0 Brazilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/openAccessTempos de entrada e retornoAproximação exponencialPoço de potencialEspectro do tempo de esperaProcessos misturadoresHitting and return timesExponential approximationPotential wellWaiting time spectrumMixing processesCIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE::TEORIA GERAL E PROCESSOS ESTOCASTICOSPoincaré recurrence times in stochastic mixing processesTempos de recorrência de Poincaré em processos estocásticos com misturainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesis600600f6880f5a-77c9-4f78-99c8-0595bf858ac0reponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8811https://repositorio.ufscar.br/bitstream/ufscar/15733/4/license_rdfe39d27027a6cc9cb039ad269a5db8e34MD54ORIGINALTese Vitor Amorim - final.pdfTese Vitor Amorim - final.pdfapplication/pdf992137https://repositorio.ufscar.br/bitstream/ufscar/15733/1/Tese%20Vitor%20Amorim%20-%20final.pdfd6300da18f7c498910acc1f9772d0d29MD51Carta comprovante PIPGEs - assinada.pdfCarta comprovante PIPGEs - assinada.pdfCarta comprovante da versão final de teses e dissertaçõesapplication/pdf146348https://repositorio.ufscar.br/bitstream/ufscar/15733/3/Carta%20comprovante%20PIPGEs%20-%20assinada.pdf4df93410d8af3c0df702665cf8afc682MD53TEXTTese Vitor Amorim - final.pdf.txtTese Vitor Amorim - final.pdf.txtExtracted texttext/plain200832https://repositorio.ufscar.br/bitstream/ufscar/15733/5/Tese%20Vitor%20Amorim%20-%20final.pdf.txtb1c1df8bb8626ae54285be318721a148MD55Carta comprovante PIPGEs - assinada.pdf.txtCarta comprovante PIPGEs - assinada.pdf.txtExtracted texttext/plain1265https://repositorio.ufscar.br/bitstream/ufscar/15733/7/Carta%20comprovante%20PIPGEs%20-%20assinada.pdf.txt7df7e26856a9b43bede0cf5a23f0e99aMD57THUMBNAILTese Vitor Amorim - final.pdf.jpgTese Vitor Amorim - final.pdf.jpgIM Thumbnailimage/jpeg15180https://repositorio.ufscar.br/bitstream/ufscar/15733/6/Tese%20Vitor%20Amorim%20-%20final.pdf.jpg083129be80c49e47721269a4097a562bMD56Carta comprovante PIPGEs - assinada.pdf.jpgCarta comprovante PIPGEs - assinada.pdf.jpgIM Thumbnailimage/jpeg7786https://repositorio.ufscar.br/bitstream/ufscar/15733/8/Carta%20comprovante%20PIPGEs%20-%20assinada.pdf.jpg05b51098ecb2cfae8c43b586ea44e609MD58ufscar/157332023-09-18 18:32:30.006oai:repositorio.ufscar.br:ufscar/15733Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:32:30Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.eng.fl_str_mv |
Poincaré recurrence times in stochastic mixing processes |
dc.title.alternative.por.fl_str_mv |
Tempos de recorrência de Poincaré em processos estocásticos com mistura |
title |
Poincaré recurrence times in stochastic mixing processes |
spellingShingle |
Poincaré recurrence times in stochastic mixing processes Amorim, Vitor Gustavo de Tempos de entrada e retorno Aproximação exponencial Poço de potencial Espectro do tempo de espera Processos misturadores Hitting and return times Exponential approximation Potential well Waiting time spectrum Mixing processes CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE::TEORIA GERAL E PROCESSOS ESTOCASTICOS |
title_short |
Poincaré recurrence times in stochastic mixing processes |
title_full |
Poincaré recurrence times in stochastic mixing processes |
title_fullStr |
Poincaré recurrence times in stochastic mixing processes |
title_full_unstemmed |
Poincaré recurrence times in stochastic mixing processes |
title_sort |
Poincaré recurrence times in stochastic mixing processes |
author |
Amorim, Vitor Gustavo de |
author_facet |
Amorim, Vitor Gustavo de |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/5021711316846807 |
dc.contributor.author.fl_str_mv |
Amorim, Vitor Gustavo de |
dc.contributor.advisor1.fl_str_mv |
Gallo, Alexsandro Giacomo Grimbert |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/4037274656833325 |
dc.contributor.advisor-co1.fl_str_mv |
Abadi, Miguel Natalio |
dc.contributor.advisor-co1Lattes.fl_str_mv |
http://lattes.cnpq.br/8422115514014109 |
dc.contributor.authorID.fl_str_mv |
f973b4f2-b626-4e5f-be42-d94bcd15c199 |
contributor_str_mv |
Gallo, Alexsandro Giacomo Grimbert Abadi, Miguel Natalio |
dc.subject.por.fl_str_mv |
Tempos de entrada e retorno Aproximação exponencial Poço de potencial Espectro do tempo de espera Processos misturadores |
topic |
Tempos de entrada e retorno Aproximação exponencial Poço de potencial Espectro do tempo de espera Processos misturadores Hitting and return times Exponential approximation Potential well Waiting time spectrum Mixing processes CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE::TEORIA GERAL E PROCESSOS ESTOCASTICOS |
dc.subject.eng.fl_str_mv |
Hitting and return times Exponential approximation Potential well Waiting time spectrum Mixing processes |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA::PROBABILIDADE::TEORIA GERAL E PROCESSOS ESTOCASTICOS |
description |
In the context of the discrete-time stochastic processes, this thesis presents new results on Poincaré recurrence theory. After a complete review of recent results, we present a new theorem on the exponential approximations for hitting and return times distributions. We show that the scaling parameter of the approximate distribution, called "potential well", brings fundamental informations about the structure of the target set. Moreover, we show that the asymptotic properties of the potential well influences several aspects of the recurrence times, such as limiting distributions and moments. Finally, we apply our results to obtain the waiting time spectrum as a function of the Rényi entropy for classes of processes not covered by previous works. |
publishDate |
2022 |
dc.date.accessioned.fl_str_mv |
2022-03-23T13:40:50Z |
dc.date.available.fl_str_mv |
2022-03-23T13:40:50Z |
dc.date.issued.fl_str_mv |
2022-02-17 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/doctoralThesis |
format |
doctoralThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
AMORIM, Vitor Gustavo de. Poincaré recurrence times in stochastic mixing processes. 2022. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/15733. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/15733 |
identifier_str_mv |
AMORIM, Vitor Gustavo de. Poincaré recurrence times in stochastic mixing processes. 2022. Tese (Doutorado em Estatística) – Universidade Federal de São Carlos, São Carlos, 2022. Disponível em: https://repositorio.ufscar.br/handle/ufscar/15733. |
url |
https://repositorio.ufscar.br/handle/ufscar/15733 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.confidence.fl_str_mv |
600 600 |
dc.relation.authority.fl_str_mv |
f6880f5a-77c9-4f78-99c8-0595bf858ac0 |
dc.rights.driver.fl_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Attribution-NonCommercial-NoDerivs 3.0 Brazil http://creativecommons.org/licenses/by-nc-nd/3.0/br/ |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa Interinstitucional de Pós-Graduação em Estatística - PIPGEs |
dc.publisher.initials.fl_str_mv |
UFSCar |
publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.source.none.fl_str_mv |
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Universidade Federal de São Carlos (UFSCAR) |
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UFSCAR |
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UFSCAR |
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Repositório Institucional da UFSCAR |
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Repositório Institucional da UFSCAR |
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