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A Markov chain associated with the minimal quasi-stationary distribution of birth–death chains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Servet Martínez  and
Maria Eulália Vares
Servet Martínez*
Affiliation:
Universidad de Chile
Maria Eulália Vares*
Affiliation:
Instituto de Matemática Pura e Aplicada, Rio de Janeiro
*
∗Postal address: Departamento de Ingeniería Matemática, Universidad de Chile, Casilla 170–3 Correo 3, Santiago, Chile.
∗∗Postal address: Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardîm Botânico, 22460 Rio de Janeiro, Brasil.
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Abstract

We show that if the limiting conditional distribution for an absorbed birth–death chain exists, then the chain conditioned to non-absorption converges to a Markov chain with transition probabilities given by the matrix associated with the minimal quasi-stationary distribution.

Keywords

YAGLOM LIMITRANDOM WALKS

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 1 , March 1995 , pp. 25 - 38
Copyright
Copyright © Applied Probability Trust 1995 

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References

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