LIMIT THEOREMS FOR STOPPED FUNCTIONALS OF MARKOV RENEWAL PROCESSES

GEROLD ALSMEYER^{1} AND ALLAN GUT^{2}

1Institut für Mathematische Statistik, Westfählische Wilhelms-Universität Münster,

Einsteinstrasse 62, D-48 149 Münster, Germany

2Department of Mathematics, Uppsala University, P.O. Box 480, S-751 06 Uppsala, Sweden

(Received June 30, 1997; revised February 23, 1998)

Abstract. Some results for stopped random walks are extended to the Markov renewal setup where the random walk is driven by a Harris recurrent Markov chain. Some interesting applications are given; for example, a generalization of the alternating renewal process.

Key words and phrases: Markov renewal process, semi-Markov process, Harris recurrent, stopped sums, m-dependence, Anscombe’s theorem, law of large numbers, central limit theorem, law of the iterated logarithm.