The occurrence of sequence patterns in ergodic Markov chains (Q791233)

This paper continues a recent line of investigation concerning the expected waiting time for the first occurrence of a fixed finite pattern in a sequence of observations \(Z_ 1,Z_ 2,..\). of i.i.d. discrete random variables. The author extends this work by allowing the successive observations to be generated by an ergodic Markov chain. In earlier work on this topic, \textit{G. Blom} [J. Appl. Probab. 19, 136-143 (1982; Zbl 0482.60012)] used renewal theory arguments and \textit{S.-Y. R. Li} [Ann. Probab. 8, 1171-1176 (1980; Zbl 0447.60006)] used a stopping time identity for martingales. The author uses the occupation measure identity for Markov chains to obtain his generalization.