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November, 1984 Conditional Markov Renewal Theory I. Finite and Denumerable State Space
S. P. Lalley
Ann. Probab. 12(4): 1113-1148 (November, 1984). DOI: 10.1214/aop/1176993144


A renewal theory is developed for sums of independent random variables whose distributions are determined by the current state of a Markov chain (also known as "Markov additive" processes, or "semi-Markov" processes). This theory departs from existing theories in that its conclusions are required to be valid conditionally for a given realization of the Markov Chain. It rests on a peculiar coupling construction which differs markedly from existing coupling arguments.


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S. P. Lalley. "Conditional Markov Renewal Theory I. Finite and Denumerable State Space." Ann. Probab. 12 (4) 1113 - 1148, November, 1984.


Published: November, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0551.60094
MathSciNet: MR757772
Digital Object Identifier: 10.1214/aop/1176993144

Primary: 60K15
Secondary: 60K05

Keywords: conditional limit theorem , coupling , Markov renewal theory

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 4 • November, 1984
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