Existence of non-trivial quasi-stationary distributions in the birth-death chain-Reference-Cited by-同舟云学术

Existence of non-trivial quasi-stationary distributions in the birth-death chain

Published:1992-12 Issue:04 Volume:24 Page:795-813
ISSN:0001-8678
Container-title:Advances in Applied Probability
language:en
Short-container-title:Adv. Appl. Probab.

Author:

Ferrari Pablo A.,Martínez Servet,Picco Pierre

Abstract

We study conditions for the existence of non-trivial quasi-stationary distributions for the birth-and-death chain with 0 as absorbing state. We reduce our problem to a continued fractions one that can be solved by using extensions of classical results of this theory. We also prove that there exist normalized quasi-stationary distributions if and only if 0 is geometrically absorbing.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Reference14 articles.

1. The classification of birth and death processes

2. The differential equations of birth-and-death processes, and the Stieltjes moment problem

3. The limiting behavior of transient birth and death processes conditioned on survival

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