Waiting times and stopping probabilities for patterns in Markov chains
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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 A ∈ C, where τ A is the waiting time until the pattern A appears as a run.
Keywordspattern Markov chain stopping probability waiting time
MR Subject Classification60J10 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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