Non-asymptotic exact distribution for hitting times

• Ano de defesa: 2020
• Autor(a) principal: Codas, Julia Faria
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Hitting time; Recurrence relation; Relação de recorrência; Tempo de entrada
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45133/tde-11082020-165440/

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.