Waiting times and stopping probabilities for patterns in Markov chains

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

13 pages