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On identifiability and order of continuous-time aggregated Markov chains, Markov-modulated Poisson processes, and phase-type distributions

Part of: Distribution theory - Probability Markov processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Tobias Rydén
Tobias Rydén*
Affiliation:
Lund Institute of Technology
*
∗Postal address: Department of Mathematical Statistics, Lund Institute of Technology, Box 118, S-221 00 Lund, Sweden.
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Abstract

An aggregated Markov chain is a Markov chain for which some states cannot be distinguished from each other by the observer. In this paper we consider the identifiability problem for such processes in continuous time, i.e. the problem of determining whether two parameters induce identical laws for the observable process or not. We also study the order of a continuous-time aggregated Markov chain, which is the minimum number of states needed to represent it. In particular, we give a lower bound on the order. As a by-product, we obtain results of this kind also for Markov-modulated Poisson processes, i.e. doubly stochastic Poisson processes whose intensities are directed by continuous-time Markov chains, and phase-type distributions, which are hitting times in finite-state Markov chains.

Keywords

AGGREGATED MARKOV CHAINHIDDEN MARKOV CHAINHIDDEN MARKOV MODELMARKOV-MODULATED POISSON PROCESSPHASE-TYPE DISTRIBUTIONIDENTIFIABILITY

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60G55: Point processes 60E99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 3 , September 1996 , pp. 640 - 653
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Supported by the National Board for Industrial and Technical Development, Grant no. 88–02060P.

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