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Spectral representations of the transition probability matrices for continuous time finite Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Nan Fu Peng
Nan Fu Peng*
Affiliation:
National Chiao Tung University
*
∗Postal address: Institute of Statistics, National Chiao Tung University, 1001 TA Hsueh Road, Hsinchu, Taiwan.
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Abstract

Using an easy linear-algebraic method, we obtain spectral representations, without the need for eigenvector determination, of the transition probability matrices for completely general continuous time Markov chains with finite state space. Comparing the proof presented here with that of Brown (1991), who provided a similar result for a special class of finite Markov chains, we observe that ours is more concise.

Keywords

MARKOV CHAINSTRANSITION PROBABILITY MATRICESSPECTRAL REPRESENTATIONS

MSC classification

Primary: 60J35: Transition functions, generators and resolvents
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 1 , March 1996 , pp. 28 - 33
Copyright
Copyright © Applied Probability Trust 1996 

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