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The deviation matrix of a continuous-time Markov chain

Coolen-Schrijner, P.; Van Doorn, E.A.

Authors

P. Coolen-Schrijner

E.A. Van Doorn



Abstract

The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P(·) and ergodic matrix [Pi] is the matrix D [identical with] [integral operator]0[infty infinity](P(t) [minus sign] [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.

Citation

Coolen-Schrijner, P., & Van Doorn, E. (2002). The deviation matrix of a continuous-time Markov chain. Probability in the Engineering and Informational Sciences, 16(3), 351-366. https://doi.org/10.1017/s0269964802163066

Journal Article Type Article
Publication Date Jul 1, 2002
Deposit Date May 22, 2008
Journal Probability in the Engineering and Informational Sciences
Print ISSN 0269-9648
Electronic ISSN 1469-8951
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 16
Issue 3
Pages 351-366
DOI https://doi.org/10.1017/s0269964802163066

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