The Annals of Probability

Conditional Markov Renewal Theory I. Finite and Denumerable State Space

S. P. Lalley

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Abstract

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.

Article information

Source
Ann. Probab., Volume 12, Number 4 (1984), 1113-1148.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993144

Digital Object Identifier
doi:10.1214/aop/1176993144

Mathematical Reviews number (MathSciNet)
MR757772

Zentralblatt MATH identifier
0551.60094

JSTOR
links.jstor.org

Subjects
Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60K05: Renewal theory

Keywords
Markov renewal theory coupling conditional limit theorem

Citation

Lalley, S. P. Conditional Markov Renewal Theory I. Finite and Denumerable State Space. Ann. Probab. 12 (1984), no. 4, 1113--1148. doi:10.1214/aop/1176993144. https://projecteuclid.org/euclid.aop/1176993144


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