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The deviation matrix of a continuous-time Markov chain.

Coolen-Schrijner, P. and Van Doorn, E. A. (2002) 'The deviation matrix of a continuous-time Markov chain.', Probability in the engineering and informational sciences., 16 (3). pp. 351-366.


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.

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Record Created:22 May 2008
Last Modified:15 Feb 2010 12:41

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