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Master's Dissertation
DOI
10.11606/D.104.2018.tde-13112018-133355
Document
Author
Full name
Milton Miranda Neto
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Gava, Renato Jacob (President)
Coletti, Cristian Favio
Diniz, Marcio Alves
Title in Portuguese
Abordagem de martingais para análise assintótica do passeio aleatório do elefante
Keywords in Portuguese
Martingais
Passeio aleatório do elefante
Processos estocásticos
Abstract in Portuguese
Neste trabalho, estudamos o passeio aleatório do elefante introduzido em (SCHUTZ; TRIMPER, 2004). Um processo estocástico não Markoviano com memória de alcance ilimitada que apresenta transição de fase. Nosso objetivo é demonstrar a convergência quase certa do passeio aleatório do elefante nos casos subcrítico e crítico. Além destes resultado, também apresentamos a demonstração do Teorema Central do Limite para ambos os regimes. Para o caso supercrítico, vamos demonstrar a convergência do passeio aleatório do elefante para uma variável aleatória não normal com base nos artigos (BAUR; BERTOIN, 2016), (BERCU, 2018) e (COLETTI; GAVA; SCHUTZ, 2017b).
Title in English
Martingale approach for asymptotic analysis of elephant random walk
Keywords in English
Elephant random walk
Martingale
Stochastic process
Abstract in English
In this work we study the elephant random walk introduced in (SCHUTZ; TRIMPER, 2004), a discrete time, non-Markovian stochastic process with unlimited range memory that presents phase transition. Our objective is to proof the almost sure convergence for the subcritical and critical regimes of the model. We also present a demonstration of the Central Limit Theorem for both regimes. For the supercritical regime we proof the convergence of the elephant random walk to a non-normal random variable based on the articles (BAUR; BERTOIN, 2016), (BERCU, 2018) and (COLETTI; GAVA; SCHUTZ, 2017b).
 
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Publishing Date
2018-11-13
 
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