Ratio limits and limiting conditional distributions for discrete-time birth-death processes

Erik A. van Doorn, Pauline Schrijner

    Research output: Contribution to journalArticleAcademicpeer-review

    16 Citations (Scopus)
    43 Downloads (Pure)

    Abstract

    We consider discrete-time birth-death processes with an absorbing state and study the conditional state distribution at time n given that absorption has not occurred by that time but will occur eventually. In particular, we establish conditions for the convergence of these distributions to a proper distribution as n→∞. The problem turns out to be closely related to that of finding conditions for the existence of limits of ratios of n-step transition probabilities as n→∞. Orthogonal polynomials feature in the spectral representation for the n-step transition probabilities of a birth-death process and, consequently, play a key role in the analysis.
    Original languageEnglish
    Pages (from-to)263-284
    Number of pages22
    JournalJournal of mathematical analysis and applications
    Volume190
    Issue number1
    DOIs
    Publication statusPublished - 1995

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