The deviation matrix of a continuous-time Markov chain

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

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
• Public URL: https://durham-repository.worktribe.com/output/1628906