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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: pauline.schrijner@durham.ac.uk
Erik A. van Doorn
Affiliation:
Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands, E-mail: doorn@math.utwente.nl
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Abstract

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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.

Information

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