Open Access
Translator Disclaimer
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

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.

Citation

Download Citation

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

Information

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

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

Subjects:
Primary: 60K15
Secondary: 60K05

Keywords: conditional limit theorem , coupling , Markov renewal theory

Rights: Copyright © 1984 Institute of Mathematical Statistics

JOURNAL ARTICLE
36 PAGES


SHARE
Vol.12 • No. 4 • November, 1984
Back to Top