Mestrado em Matemática

URI Permanente para esta coleção

http://repositorio.ufes.br/handle/10/17496

Nível: Mestrado Acadêmico
Ano de início: 2006
Conceito atual na CAPES: 3
Ato normativo: Homologado pelo CNE ( Port. MEC 609, de 14/03/2019, DOU 18/03/2019)
Periodicidade de seleção: Anual
Área(s) de concentração: Matemática
Url do curso: https://matematica.ufes.br/pt-br/pos-graduacao/PPGMAT/detalhes-do-curso?id=1401

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Navegando Mestrado em Matemática por Autor "Bessam, Diogo Manuel Fernandes"

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    Perfil do cutoff do processo de exclusão no grafo completo
    (Universidade Federal do Espírito Santo, 2024-04-15) Oliveira, Éric Santana; Jara Valenzuela, Milton David; https://orcid.org/; http://lattes.cnpq.br/7496571533341165; Silva, Fábio Júlio da ; https://orcid.org/0000-0003-2405-7696; http://lattes.cnpq.br/8745134398831488; https://orcid.org/; http://lattes.cnpq.br/4639522148187770; Bessam, Diogo Manuel Fernandes ; https://orcid.org/; http://lattes.cnpq.br/2356936612360198; Hernandez Romero, Freddy Rolando ; https://orcid.org/0000-0001-5410-3062; http://lattes.cnpq.br/2961243559975382
    This dissertation delves into the study of Markov chains, evolutionary processes characterized by “memory loss”, widely applied in diverse fields such as biology, statistics, and finance. The convergence of these chains to a stationary distribution is analyzed using the “total variation distance”. The times of 𝜀-mixing are introduced, representing the time required for convergence. The concept of coupling between Markov chains is presented, demonstrating its utility in de termining bounds for mixing times. The phenomenon of cutoff, an abrupt decrease in total variation distance, is explored, providing a detailed understanding of convergence. The ulti mate goal is to calculate the cutoff profile for the simple exclusion processes on complete graphs. Chapters cover the construction of chains, technical concepts, couplings, and mixing times, cul minating in the analysis of the cutoff phenomenon and its specific application to the exclusion process in the complete graph
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    Uma introdução a grandes desvios com aplicações em finanças quantitativa
    (Universidade Federal do Espírito Santo, 2022-12-21) Moreira, Vinicio Rodrigues; Valentim, Fabio Julio da Silva; https://orcid.org/0000000324057696; http://lattes.cnpq.br/8745134398831488; http://lattes.cnpq.br/0376726756334144 ; Coelho, Glauco Valle da Silva; https://orcid.org/0000-0002-3823-8220; http://lattes.cnpq.br/3059644734308048 ; Bessam, Diogo Manuel Fernandes; http://lattes.cnpq.br/2356936612360198
    In this dissertation we will introduce the reader to The Theory of Large Deviations. We will develop results that will allow us to estimate the decay rate of the probability of an event, as well as an introduction to an application in quantitative finance. The main results of this work are Sanov’s Theorem, which allows us to study the decay speed of probabilities in a finite set, Crámer’s Theorem, which allows us to study the decay speed of probabilities in R, and a Theorem in the Sanov’s Theorem, which introduces us to the study of Losses in Large Risk Credit Portfolios.