## The Annals of Probability

### Renewal Theory for Markov Chains on the Real Line

Robert W. Keener

#### 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.

#### Article information

Source
Ann. Probab., Volume 10, Number 4 (1982), 942-954.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176993716

Digital Object Identifier
doi:10.1214/aop/1176993716

Mathematical Reviews number (MathSciNet)
MR672295

Zentralblatt MATH identifier
0498.60087

JSTOR