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Similar Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

P. K. Pollett
P. K. Pollett*
Affiliation:
University of Queensland
*
1Postal address: Dept Mathematics, The University of Queensland Qld 4072, Australia. Email: pkp@maths.uq.edu.au
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Abstract

Lenin et al. (2000) recently introduced the idea of similarity in the context of birth-death processes. This paper examines the extent to which their results can be extended to arbitrary Markov chains. It is proved that, under a variety of conditions, similar chains are strongly similar in a sense which is described, and it is shown that minimal chains are strongly similar if and only if the corresponding transition-rate matrices are strongly similar. A general framework is given for constructing families of strongly similar chains; it permits the construction of all such chains in the irreducible case.

Keywords

Invariant measuresbirth-death processessimilar Markov chains

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J35: Transition functions, generators and resolvents
Type
Markov chains
Information
Journal of Applied Probability , Volume 38 , Issue A: Probability, Statistics and Seismology , 2001 , pp. 53 - 65
Copyright
Copyright © Applied Probability Trust 2001 

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