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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2020.tde-11082020-165440
Document
Author
Full name
Julia Faria Codas
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Abadi, Miguel Natalio (President)
Gallo, Alexsandro Giacomo Grimbert
Mora, Erika Alejandra Rada
Title in English
Non-asymptotic exact distribution for hitting times
Keywords in English
Hitting time
Recurrence relation
Abstract in English
The time elapsed until the first occurrence of an observable in a realization of a stochastic process is a classic object of study. It is a known result that the distribution of the hitting time, when properly rescaled, converges to an exponential law. In this work, we present the exact form of the distribution of the hitting time of a fixed finite sequence in an independent and identically distributed process, which is defined over a finite or countable alphabet. That is, we get the result that is not just asymptotic. We show that the exact distribution of the hitting time is a sum of exponentials. We prove that this sum has a dominant term and that the others converge to zero.
Title in Portuguese
Distribuição exata não assintótica de tempos de entrada
Keywords in Portuguese
Relação de recorrência
Tempo de entrada
Abstract in Portuguese
O tempo decorrido até a primeira ocorrência de um observável em uma realização de um processo estocástico é um objeto de estudo clássico. É conhecido que a distribuição do tempo de entrada, quando reescalada adequadamente, converge para uma lei exponencial. Neste trabalho, apresentamos a forma exata da distribuição do tempo de entrada de uma sequência finita fixa em um processo independente e identicamente distribuído, e definido sobre um alfabeto finito ou enumerável. Isto é, obtemos o resultado que não é apenas assintótico. Mostramos que a distribuição exata do tempo de entrada é uma soma de exponenciais. Provamos que esta soma possui um termo dominante e que os demais convergem para zero.
 
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dissertacao.pdf (571.15 Kbytes)
Publishing Date
2021-02-04
 
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