Tempo de espera para a ocorrência de palavras em ensaios de Markov

Abstract

Consider a sequence of independent coin flips where we denote the result of any landing for H, if coming up head, or T, otherwise. Create patterns with H's and T's, for example, HHHHH or HTHTH. How many times do we have to land the same coin until one such two patterns happens? For example, let the sequences being THTHHHHH and TTHTTHTHTH. The number of times that we landed the coin until HHHHH and HTHTH happens it was eight and ten times respectively. We can generalize this idea for a finite number of patterns in any nite set. Then, the rst of all interest of this dissertation is to nd the distribution of the waiting time until a member of a nite colection of patterns is observed in a sequence of Markov chains of letters in from finite set. More speci cally the letters in a nite set are generated by Markov chain until one of the patterns in any fi nite set happens. Besides that, we will find the probability of a pattern happen before of all patterns in the same nite set. Finally we will find the generator function of probability of waiting time.