Waiting times and stopping probabilities for patterns in Markov chains
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.
关键词：
pattern,
Markov chain,
stopping probability,
waiting time
