The deviation matrix of a continuous-time Markov chain

Pauline Coolen-Schrijner, Erik A. van Doorn

    Research output: Contribution to journalArticleAcademicpeer-review

    42 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

    Fingerprint

    Continuous-time Markov Chain
    Markov processes
    Deviation
    Pi
    Birth-death Process
    Transition Probability Matrix
    Stationarity
    Continuous-time Markov chain
    Markov chain

    Keywords

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

    Cite this

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    title = "The deviation matrix of a continuous-time Markov chain",
    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.",
    keywords = "Birth-death process, ergodic Markov chain, deviation matrix, convergence to stationarity, IR-62339, EWI-12837, METIS-206668",
    author = "Pauline Coolen-Schrijner and {van Doorn}, {Erik A.}",
    year = "2002",
    doi = "10.1017/S0269964802163066",
    language = "English",
    volume = "16",
    pages = "351--366",
    journal = "Probability in the engineering and informational sciences",
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    }

    The deviation matrix of a continuous-time Markov chain. / Coolen-Schrijner, Pauline; van Doorn, Erik A.

    In: Probability in the engineering and informational sciences, Vol. 16, No. 3, 2002, p. 351-366.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - The deviation matrix of a continuous-time Markov chain

    AU - Coolen-Schrijner, Pauline

    AU - van Doorn, Erik A.

    PY - 2002

    Y1 - 2002

    N2 - 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.

    AB - 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.

    KW - Birth-death process

    KW - ergodic Markov chain

    KW - deviation matrix

    KW - convergence to stationarity

    KW - IR-62339

    KW - EWI-12837

    KW - METIS-206668

    U2 - 10.1017/S0269964802163066

    DO - 10.1017/S0269964802163066

    M3 - Article

    VL - 16

    SP - 351

    EP - 366

    JO - Probability in the engineering and informational sciences

    JF - Probability in the engineering and informational sciences

    SN - 0269-9648

    IS - 3

    ER -