Quasi-stationary distributions for a class of discrete-time Markov chains

Pauline Coolen-Schrijner, Erik A. van Doorn

    Research output: Contribution to journalArticleAcademicpeer-review

    13 Citations (Scopus)

    Abstract

    This paper is concerned with the circumstances under which a discrete-time absorbing Markov chain has a quasi-stationary distribution. We showed in a previous paper that a pure birth-death process with an absorbing bottom state has a quasi-stationary distribution -- actually an infinite family of quasi-stationary distributions -- if and only if absorption is certain and the chain is geometrically transient. If we widen the setting by allowing absorption in one step (killing) from any state, the two conditions are still necessary, but no longer sufficient. We show that the birth-death-type of behaviour prevails as long as the number of states in which killing can occur is finite. But if there are infinitely many such states, and if the chain is geometrically transient and absorption certain, then there may be 0, 1, or infinitely many quasi-stationary distributions. Examples of each type of behaviour are presented. We also survey and supplement the theory of quasi-stationary distributions for discrete-time Markov chains in general.
    Original languageEnglish
    Pages (from-to)449-465
    Number of pages17
    JournalMethodology and computing in applied probability
    Volume8
    Issue number4
    DOIs
    Publication statusPublished - 1 Dec 2006

    Keywords

    • MSC-60J80
    • METIS-238263
    • EWI-7689
    • IR-63615
    • MSC-60J10

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