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arXiv · 1602.06512

Waiting times and stopping probabilities for patterns in Markov chains

Min-Zhi Zhao·Dong Xu·Hui-Zeng Zhang
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Abstract

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 $\tau$. In this paper, we aim to give an easy way to calculate the mean waiting time $E(\tau)$ and the stopping probabilities $P(\tau=\tau_A)$ with $A\in\mathcal C$, where $\tau_A$ is the waiting time until the pattern $A$ appears as a run.

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Min-Zhi Zhao, Dong Xu, Hui-Zeng Zhang. 2016-02-21. Waiting times and stopping probabilities for patterns in Markov chains. https://arxiv.org/abs/1602.06512

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