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LIMIT THEOREMS FOR STOPPED FUNCTIONALS

OF MARKOV RENEWAL PROCESSES

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

^{1} *Institut für Mathematische Statistik, Westfählische Wilhelms-Universität Münster,*

Einsteinstrasse 62, D-48 149 Münster, Germany

^{2} *Department 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.

**Source**
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