Weak convergence of conditioned birth-death processes in discrete time

Pauline Coolen-Schrijner, Erik A. van Doorn

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    Abstract

    We consider a discrete-time birth-death process on the nonnegative integers with -1 as an absorbing state and study the limiting behaviour as $n \to \infty$ of the process conditioned on nonabsorption until time $n$. By proving that a condition recently proposed by Martinez and Vares is vacuously true, we establish that the conditioned process is always weakly convergent when all self-transition probabilities are zero. In the aperiodic case we obtain a necessary and sufficient condition for weak convergence.
    Original languageEnglish
    Pages (from-to)46-53
    Number of pages12
    JournalJournal of applied probability
    Volume34
    Issue number34
    DOIs
    Publication statusPublished - 1997

    Keywords

    • EWI-12860
    • IR-62355
    • METIS-140771

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