Waiting times and stopping probabilities for patterns in Markov chains

2016/02/21 by Min-Zhi Zhao, Dong Xu, Zhao, Min-Zhi +3
Mathematics · #60J10 #60J22 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60J10 #msc:60J22

paper · pdf · doi:10.48550/arxiv.1602.06512

13 pages

arxiv created 2017/02/20 · arxiv updated 2017/02/21

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 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∈\mathcal C, where τ_A is the waiting time until the pattern A appears as a run.

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