Poincaré recurrence times in stochastic mixing processes

Detalhes bibliográficos
Autor(a) principal: Amorim, Vitor Gustavo de
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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spelling 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
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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.
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/
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http://creativecommons.org/licenses/by-nc-nd/3.0/br/
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dc.publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
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dc.publisher.initials.fl_str_mv UFSCar
publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
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