Geomatric ergodicity and quasi-stationarity in discrete-time birth-death processes
- 1 October 1995
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of the Australian Mathematical Society. Series B. Applied Mathematics
- Vol. 37 (2), 121-144
- https://doi.org/10.1017/s0334270000007621
Abstract
We study two aspects of discrete-time birth-death processes, the common feature of which is the central role played by the decay parameter of the process. First, conditions for geometric ergodicity and bounds for the decay parameter are obtained. Then the existence and structure of quasi-stationary distributions are discussed. The analyses are based on the spectral representation for the n-step transition probabilities of a birth-death process developed by Karlin and McGregor.Keywords
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