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November, 1982 Renewal Theory for Markov Chains on the Real Line
Robert W. Keener
Ann. Probab. 10(4): 942-954 (November, 1982). DOI: 10.1214/aop/1176993716

Abstract

Standard renewal theory is concerned with expectations related to sums of positive i.i.d. variables, $S_n = \sum^n_{i=1} Z_i$. We generalize this theory to the case where $\{S_i\}$ is a Markov chain on the real line with stationary transition probabilities satisfying a drift condition. The expectations we are concerned with satisfy generalized renewal equations, and in our main theorems, we show that these expectations are the unique solutions of the equations they satisfy.

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Robert W. Keener. "Renewal Theory for Markov Chains on the Real Line." Ann. Probab. 10 (4) 942 - 954, November, 1982. https://doi.org/10.1214/aop/1176993716

Information

Published: November, 1982
First available in Project Euclid: 19 April 2007

zbMATH: 0498.60087
MathSciNet: MR672295
Digital Object Identifier: 10.1214/aop/1176993716

Subjects:
Primary: 62L05
Secondary: 62K20

Keywords: Markov chains , Random walks , renewal theory

Rights: Copyright © 1982 Institute of Mathematical Statistics

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Vol.10 • No. 4 • November, 1982
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