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THE DEVIATION MATRIX OF A CONTINUOUS-TIME MARKOV CHAIN

Published online by Cambridge University Press:  22 May 2002

Pauline Coolen-Schrijner  and
Erik A. van Doorn
Pauline Coolen-Schrijner
Affiliation:
Department of Mathematical Sciences, University of Durham, Durham, UK, E-mail: [email protected]
Erik A. van Doorn
Affiliation:
Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands, E-mail: [email protected]
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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.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 16 , Issue 3 , July 2002 , pp. 351 - 366
Copyright
© 2002 Cambridge University Press

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