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

Damian Clancy, Philip Pollett

Research output: Contribution to journalArticle

20 Citations (Scopus)

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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