Stochastic processes and random matrices
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2021 |
| Tipo de documento: | Tese |
| Idioma: | eng |
| Título da fonte: | Repositório Institucional da UFPE |
| Texto Completo: | https://repositorio.ufpe.br/handle/123456789/39792 |
Resumo: | OSPINA MARTÍNEZ, Raydonal também é conhecido em citações bibliográficas por: MARTÍNEZ, Raydonal Ospina e OSPINA, Raydonal |
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ALBUQUERQUE, Roberta Rodrigueshttp://lattes.cnpq.br/9619148595653487http://lattes.cnpq.br/6357960802605841http://lattes.cnpq.br/7160030619369816OSPINA MARTÍNEZ, RaydonalMACÊDO, Antônio Murilo Santos2021-04-19T18:15:52Z2021-04-19T18:15:52Z2021-02-24ALBUQUERQUE, Roberta Rodrigues. Stochastic processes and random matrices. 2021. Tese (Doutorado em Estatística) – Universidade Federal de Pernambuco, Recife, 2021.https://repositorio.ufpe.br/handle/123456789/39792OSPINA MARTÍNEZ, Raydonal também é conhecido em citações bibliográficas por: MARTÍNEZ, Raydonal Ospina e OSPINA, RaydonalThe thesis is divided in three main parts which can be read independetly and in any order. In the first part we consider the exchangeable random partitions and its relation with the coalescent processes which gives a coalescent tree. We found (1) a new proof of the consistency of infinite exchangeable random partions (2) A reformulation of the Λ-coalescent theorem (3) an connection of the exchangeable random partitions and coalescent processes with mutations. This connection is given by the Möhle formula. In the second part we consider a left invariant stochastic differential equation on the on the Heisenberg Lie group which correspond to an hypoelliptic operator. We found (1) a integration by parts formula on the space of paths of the Heisenberg Lie group and (2) the Bismut type formula. In the third part there is a short scale distribution which is obtained from a compound of distributions: the conditional and the background distributions. In our problem, we consider the Gaussian distribution as the conditional and the Wishart distribution as the background. We found (1) a new proof of the convolution theorem. (2) we calculate the -transform of the Gaussian and Wishart distributions and apply the convolution theorem to obtain the compound of the distributions.CAPESA tese está dividida em três partes principais que podem ser lidas de forma independente e em qualquer ordem. Na primeira parte consideramos as partições aleatórias permutáveis e sua relação com os processos coalescentes, estes geram uma árvore coalescente. Temos (1) uma prova alternativa da consistência de partições aleatórias permutáveis infinitas (2) uma reformulação do teorema Λ-coalescente (3) uma conexão das partições aleatórias permutáveis e processos coalescentes com mutações. Esta conexão é dada pela fórmula Möhle. Na segunda parte, consideramos uma equação diferencial estocástica invariante à esquerda no grupo de Lie de Heisenberg que corresponde a um operador hipoelíptico. Temos (1) uma fórmula de integração por partes no espaço de caminhos do grupo de Lie de Heisenberg e (2) a fórmula do tipo Bismut. Na terceira parte, há uma distribuição de escala curta que é obtida a partir de um composto de distribuições: a distribuição condicional e a distribuição de fundo. Em nosso problema, consideramos a distribuição Gaussiana como condicional e a distribuição de Wishart como pano de fundo. Temos (1) uma nova prova do teorema da convolução (2) calculamos a transformação das distribuições Gaussiana e de Wishart e aplicamos o teorema da convolução para obter o composto das distribuições.engUniversidade Federal de PernambucoPrograma de Pos Graduacao em EstatisticaUFPEBrasilhttp://creativecommons.org/licenses/by-nc-nd/3.0/br/info:eu-repo/semantics/embargoedAccessProbabilidadeEquações diferenciaisStochastic processes and random matricesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisdoutoradoreponame:Repositório Institucional da UFPEinstname:Universidade Federal de Pernambuco (UFPE)instacron:UFPETEXTTESE Roberta Rodrigues Albuquerque.pdf.txtTESE Roberta Rodrigues Albuquerque.pdf.txtExtracted texttext/plain180790https://repositorio.ufpe.br/bitstream/123456789/39792/4/TESE%20Roberta%20Rodrigues%20Albuquerque.pdf.txt6754fb4fabeff7dce47556b889da45a5MD54THUMBNAILTESE Roberta Rodrigues Albuquerque.pdf.jpgTESE Roberta Rodrigues Albuquerque.pdf.jpgGenerated Thumbnailimage/jpeg1216https://repositorio.ufpe.br/bitstream/123456789/39792/5/TESE%20Roberta%20Rodrigues%20Albuquerque.pdf.jpg98a24045366dd45f1b2370962fcb09d6MD55ORIGINALTESE Roberta Rodrigues Albuquerque.pdfTESE Roberta Rodrigues Albuquerque.pdfapplication/pdf1480623https://repositorio.ufpe.br/bitstream/123456789/39792/1/TESE%20Roberta%20Rodrigues%20Albuquerque.pdfa23132267409cac24a63da6b05b8763bMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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| dc.title.pt_BR.fl_str_mv |
Stochastic processes and random matrices |
| title |
Stochastic processes and random matrices |
| spellingShingle |
Stochastic processes and random matrices ALBUQUERQUE, Roberta Rodrigues Probabilidade Equações diferenciais |
| title_short |
Stochastic processes and random matrices |
| title_full |
Stochastic processes and random matrices |
| title_fullStr |
Stochastic processes and random matrices |
| title_full_unstemmed |
Stochastic processes and random matrices |
| title_sort |
Stochastic processes and random matrices |
| author |
ALBUQUERQUE, Roberta Rodrigues |
| author_facet |
ALBUQUERQUE, Roberta Rodrigues |
| author_role |
author |
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http://lattes.cnpq.br/9619148595653487 |
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http://lattes.cnpq.br/6357960802605841 |
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http://lattes.cnpq.br/7160030619369816 |
| dc.contributor.author.fl_str_mv |
ALBUQUERQUE, Roberta Rodrigues |
| dc.contributor.advisor1.fl_str_mv |
OSPINA MARTÍNEZ, Raydonal |
| dc.contributor.advisor-co1.fl_str_mv |
MACÊDO, Antônio Murilo Santos |
| contributor_str_mv |
OSPINA MARTÍNEZ, Raydonal MACÊDO, Antônio Murilo Santos |
| dc.subject.por.fl_str_mv |
Probabilidade Equações diferenciais |
| topic |
Probabilidade Equações diferenciais |
| description |
OSPINA MARTÍNEZ, Raydonal também é conhecido em citações bibliográficas por: MARTÍNEZ, Raydonal Ospina e OSPINA, Raydonal |
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2021 |
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2021-04-19T18:15:52Z |
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2021-04-19T18:15:52Z |
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2021-02-24 |
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info:eu-repo/semantics/doctoralThesis |
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ALBUQUERQUE, Roberta Rodrigues. Stochastic processes and random matrices. 2021. Tese (Doutorado em Estatística) – Universidade Federal de Pernambuco, Recife, 2021. |
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https://repositorio.ufpe.br/handle/123456789/39792 |
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ALBUQUERQUE, Roberta Rodrigues. Stochastic processes and random matrices. 2021. Tese (Doutorado em Estatística) – Universidade Federal de Pernambuco, Recife, 2021. |
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