The deviation matrix of a continuous-time Markov chain

Pauline Coolen-Schrijner, Erik A. van Doorn

    Research output: Contribution to journalArticleAcademicpeer-review

    46 Citations (Scopus)

    Abstract

    he 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
    Pages (from-to)351-366
    Number of pages15
    JournalProbability in the engineering and informational sciences
    Volume16
    Issue number3
    DOIs
    Publication statusPublished - 2002

    Keywords

    • Birth-death process
    • ergodic Markov chain
    • deviation matrix
    • convergence to stationarity
    • IR-62339
    • EWI-12837
    • METIS-206668

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