A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic
Damian Clancy and Philip K. Pollett
Source: J. Appl. Probab.
Volume 40, Number 3
(2003), 821-825.
Abstract
For Markov processes on the positive integers with the origin as
an absorbing state, Ferrari, Kesten, Martínez and Picco
studied the existence of quasi-stationary and limiting conditional
distributions by characterizing quasi-stationary distributions as
fixed points of a transformation Φ on the space of
probability distributions on {1, 2,...}. In the case of a
birth-death process, the components of Φ(ν) can be
written down explicitly for any given distribution ν. Using
this explicit representation, we will show that Φ preserves
likelihood ratio ordering between distributions. A conjecture of
Kryscio and Lefèvre concerning the quasi-stationary
distribution of the SIS logistic epidemic follows as a corollary.
Primary Subjects: 60J27
Secondary Subjects: 60J80
Keywords: Likelihood ratio ordering; stochastic ordering; limiting conditional distribution
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jap/1059060909
Digital Object Identifier: doi:10.1239/jap/1059060909
Mathematical Reviews number (MathSciNet):
MR1993274
Zentralblatt MATH identifier:
02066258
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