Hitting times of sequences (Q1093250)

Let \(\{X_ n\), \(n=1,2,...\}\) be an ergodic Markov chain on a finite state space S, and let s and t be finite sequences of elements from S. In this paper the author determines a formula for the expected time of completing t given that s has just been observed. This formula is quite similar to a formula obtained by Li when \(\{X_ n\), \(n=1,2,...\}\), instead of being an ergodic Markov chain, is a sequence of independent identically distributed stochastic variables [see \textit{S.-Y. R. Li}, Ann. Probab. 8, 1171-1176 (1980; Zbl 0447.60006)]. The author also shows how his formula can be used for computing the hitting distribution of a set A consisting of finite sequences in S.