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Stopping Probabilities for Patterns in Markov Chains

Published online by Cambridge University Press:  30 January 2018

Renato Jacob Gava*
Affiliation:
Universidade de São Paulo
Danilo Salotti*
Affiliation:
Fundação Educacional Inaciana Padre Sabóia de Medeiros
*
Postal address: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão 1010, CEP 05508-090, São Paulo, SP, Brazil. Email address: [email protected]
∗∗ Postal address: Centro Universitário da FEI, Av. Humberto de Alencar Castelo Branco 3972, CEP 09850-901, São Bernardo do Campo, SP, Brazil. Email address: [email protected]
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Abstract

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Consider a sequence of Markov-dependent trials where each trial produces a letter of a finite alphabet. Given a collection of patterns, we look at this sequence until one of these patterns appears as a run. We show how the method of gambling teams can be employed to compute the probability that a given pattern is the first pattern to occur.

Type
Research Article
Copyright
© Applied Probability Trust 

Footnotes

Research supported by FAPESP fellowship 2012/01432-9.

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