On the Range of a Regenerative Sequence

P. W. Glynn

Stochastic Processes and Their Applications, Vol. 20, 105-113 (1985)

For a given countable partition of the range of a regenerative sequence {Xn: n≥0}, let Rn be the number of distinct sets in the partition visited by X up to time n. We study convergence issues associated with the range sequence {Rn: n≥0}. As an application, we generalize a theorem of Chosid and Isaac to Harris recurrent Markov chains.