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Waiting times and stopping probabilities for patterns in Markov chains
Min-Zhi Zhao, Dong Xu, Hui-Zeng Zhang · 2016-02-21 · via math.PR updates on arXiv.org

Suppose that $\mathcal C$ is a finite collection of patterns. Observe a Markov chain until one of the patterns in $\mathcal C$ 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 $A\in\mathcal C$, where $τ_A$ is the waiting time until the pattern $A$ appears as a run.

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