Geometric ergodicity and quasi-stationarity in discrete-time birth-death processes

Erik A. van Doorn; Pauline Schrijner

doi:10.1017/S0334270000007621

Geometric ergodicity and quasi-stationarity in discrete-time birth-death processes

Erik A. van Doorn, Pauline Schrijner

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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

Original language	English
Pages (from-to)	121-144
Number of pages	24
Journal	Journal of the Australian Mathematical Society. Series B, Applied mathematics (Online)
Volume	37
DOIs	https://doi.org/10.1017/S0334270000007621
Publication status	Published - 1995

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METIS-140704

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10.1017/S0334270000007621

Doorn1995geometricFinal published version, 1 MB

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title = "Geometric ergodicity and quasi-stationarity in discrete-time birth-death processes",

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",

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AU - van Doorn, Erik A.

AU - Schrijner, Pauline

PY - 1995

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AB - 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

KW - METIS-140704

U2 - 10.1017/S0334270000007621

DO - 10.1017/S0334270000007621

M3 - Article

SN - 1839-4078

VL - 37

SP - 121

EP - 144

JO - Journal of the Australian Mathematical Society. Series B, Applied mathematics (Online)

JF - Journal of the Australian Mathematical Society. Series B, Applied mathematics (Online)

ER -

Geometric ergodicity and quasi-stationarity in discrete-time birth-death processes

Abstract

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