The deviation matrix of a continuous-time Markov chain

P. Coolen-Schrijner, E.A. van Doorn

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    Abstract

    The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix $P(.)$ and ergodic matrix $\Pi$ is the matrix $D \equiv \int_0^{\infty} (P(t)-\Pi)dt$. We give conditions for $D$ to exist and discuss properties and a representation of $D$. The deviation matrix of a birth-death process is investigated in detail. We also describe a new application of deviation matrices by showing that a measure for the convergence to stationarity of a stochastically increasing Markov chain can be expressed in terms of the elements of the deviation matrix of the chain.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages20
    Publication statusPublished - 2001

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1567
    ISSN (Print)0169-2690

    Keywords

    • EWI-3387
    • MSC-60J10
    • IR-65754
    • MSC-60J35
    • MSC-60J80
    • MSC-60J27

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