Birth-death processes with killing: orthogonal polynomials and quasi-stationary distributions

Pauline Coolen-Schrijner, Erik A. van Doorn

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    Abstract

    The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state ({\em killing}) is possible from any state rather than just one state. The purpose of this paper is to investigate to what extent properties of birth-death processes, in particular with regard to the existence of quasi-stationary distributions, remain valid in the generalized setting. It turns out that the elegant structure of the theory of quasi-stationarity for birth-death processes remains intact as long as killing is possible from only finitely many states, but breaks down otherwise.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages18
    Publication statusPublished - 2005

    Publication series

    NameMemorandum
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1765
    ISSN (Print)0169-2690

    Keywords

    • MSC-42C05
    • MSC-60J27
    • IR-65949
    • EWI-3585
    • METIS-224146
    • MSC-60J80

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