The deviation matrix of a continuous-time Markov chain

Pauline Coolen-Schrijner; Erik A. van Doorn

doi:10.1017/S0269964802163066

The deviation matrix of a continuous-time Markov chain

Pauline Coolen-Schrijner
, Erik A. van Doorn

Research output: Contribution to journal › Article › Academic › peer-review

67 Citations (Scopus)

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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 language	English
Pages (from-to)	351-366
Number of pages	15
Journal	Probability in the engineering and informational sciences
Volume	16
Issue number	3
DOIs	https://doi.org/10.1017/S0269964802163066
Publication status	Published - 2002

Keywords

Birth-death process
Ergodic Markov chain
Deviation matrix
Convergence to stationarity

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10.1017/S0269964802163066

The deviation matrix of a continuous-time Markov chain
Coolen-Schrijner, P. & van Doorn, E. A., 2001, Enschede: University of Twente. 20 p. (Memorandum / Department of Applied Mathematics; no. 1567)
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abstract = "he deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix \$P(.)\$ and ergodic matrix \$\textbackslash{}Pi\$ is the matrix \$D \textbackslash{}equiv \textbackslash{}int\_0\textasciicircum{}\{\textbackslash{}infty\} (P(t)-\textbackslash{}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",

author = "Pauline Coolen-Schrijner and \{van Doorn\}, \{Erik A.\}",

year = "2002",

doi = "10.1017/S0269964802163066",

language = "English",

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

AU - Coolen-Schrijner, Pauline

AU - van Doorn, Erik A.

PY - 2002

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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

U2 - 10.1017/S0269964802163066

DO - 10.1017/S0269964802163066

M3 - Article

SN - 0269-9648

VL - 16

SP - 351

EP - 366

JO - Probability in the engineering and informational sciences

JF - Probability in the engineering and informational sciences

IS - 3

ER -

The deviation matrix of a continuous-time Markov chain

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The deviation matrix of a continuous-time Markov chain

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