Extinction probability in a birth-death process with killing

Erik A. van Doorn, Alexander I. Zeifman

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    Abstract

    We study birth-death processes on the nonnegative integers, where {1,2,...} is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 may occur from any state. We give a condition for absorption (extinction) to be certain and obtain the eventual absorption probabilities when absorption is not certain. We also study the rate of convergence, as t → ∞, of the probability of absorption at time t, and relate it to the common rate of convergence of the transition probabilities that do not involve state 0. Finally, we derive upper and lower bounds for the probability of absorption at time t by applying a technique that involves the logarithmic norm of an appropriately defined operator.
    Original languageUndefined
    Pages (from-to)185-198
    Number of pages14
    JournalJournal of applied probability
    Volume42
    Issue number1
    DOIs
    Publication statusPublished - 2005

    Keywords

    • IR-51051
    • METIS-223996
    • EWI-1663

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