A note on quasi-stationary distributions of birth-death processes and the SIS logistic epidemic

Damian Clancy, Philip Pollett

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)821-825
Number of pages5
JournalJournal of Applied Probability
Volume40
DOIs
Publication statusPublished - 2003

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