Geometric renewal convergence rates from hazard rates
- 1 March 2001
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 38 (01) , 180-194
- https://doi.org/10.1017/s0021900200018593
Abstract
This paper studies the geometric convergence rate of a discrete renewal sequence to its limit. A general convergence rate is first derived from the hazard rates of the renewal lifetimes. This result is used to extract a good convergence rate when the lifetimes are ordered in the sense of new better than used or increasing hazard rate. A bound for the best possible geometric convergence rate is derived for lifetimes having a finite support. Examples demonstrating the utility and sharpness of the results are presented. Several of the examples study convergence rates for Markov chains.Keywords
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