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THE DEVIATION MATRIX OF A CONTINUOUS-TIME MARKOV CHAIN

THE DEVIATION MATRIX OF A CONTINUOUS-TIME MARKOV CHAIN The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P(·) and ergodic matrix Π is the matrix D ≡ ∫0∞(P(t) − Π) 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Probability in the Engineering and Informational Sciences Cambridge University Press

THE DEVIATION MATRIX OF A CONTINUOUS-TIME MARKOV CHAIN

Probability in the Engineering and Informational Sciences , Volume 16 (3): 16 – May 22, 2002

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Publisher
Cambridge University Press
Copyright
© 2002 Cambridge University Press
ISSN
1469-8951
eISSN
0269-9648
DOI
10.1017/S0269964802163066
Publisher site
See Article on Publisher Site

Abstract

The deviation matrix of an ergodic, continuous-time Markov chain with transition probability matrix P(·) and ergodic matrix Π is the matrix D ≡ ∫0∞(P(t) − Π) 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.

Journal

Probability in the Engineering and Informational SciencesCambridge University Press

Published: May 22, 2002

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