Waiting times and stopping probabilities for patterns in Markov chains



Suppose that C is a finite collection of patterns. Observe a Markov chain until one of the patterns in C occurs as a run. This time is denoted by τ. In this paper, we aim to give an easy way to calculate the mean waiting time E(τ ) and the stopping probabilities P(τ = τ A ) with AC, where τ A is the waiting time until the pattern A appears as a run.


pattern Markov chain stopping probability waiting time 

MR Subject Classification

60J10 60J22 


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The authors wish to express their thanks to the referee for his/her constructive suggestions and many helpful comments.


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Copyright information

© Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesZhejiang UniversityHangzhouChina
  2. 2.Department of MathematicsHangzhou Normal UniversityHangzhouChina

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