Survival in a quasi-death process

Erik A. van Doorn, Philip K. Pollett

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    Abstract

    We consider a Markov chain in continuous time with an absorbing coffin state and a finite set $S$ of transient states. When $S$ is irreducible the limiting distribution of the chain as $t \to\infty,$ conditional on survival up to time $t,$ is known to equal the (unique) quasi-stationary distribution of the chain. We address the problem of generalizing this result to a setting in which $S$ may be reducible, and obtain a complete solution if the eigenvalue with maximal real part of the generator of the (sub)Markov chain on $S$ has multiplicity one. The result is applied to pure death processes and, more generally, to quasi-death processes.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages14
    Publication statusPublished - Jan 2007

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1/1815
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • limiting conditional distribution
    • MSC-60J27
    • Absorbing Markov chain
    • Quasi-stationary distribution
    • EWI-8237
    • survival-time distribution
    • death process
    • METIS-241734
    • IR-66636

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