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A canonical representation for aggregated Markov processes

Part of:Markov processes

Published online by Cambridge University Press:  14 July 2016

Bret Larget
Bret Larget*
Affiliation:
Duquesne University
*
∗ Postal address: Department of Mathematics and Computer Science, Duquesne University, College Hall 440, Pittburgh, PA 15282–1704, USA. E-mail address: larget@mathcs.duq.edu
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Abstract

A deterministic function of a Markov process is called an aggregated Markov process. We give necessary and sufficient conditions for the equivalence of continuous-time aggregated Markov processes. For both discrete- and continuous-time, we show that any aggregated Markov process which satisfies mild regularity conditions can be directly converted to a canonical representation which is unique for each class of equivalent models, and furthermore, is a minimal parameterization of all that can be identified about the underlying Markov process. Hidden Markov models on finite state spaces may be framed as aggregated Markov processes by expanding the state space and thus also have canonical representations.

Keywords

Aggregated Markov processcanonical representationhidden Markov modelidentifiabilityequivalenceminimal parameterization

MSC classification

Primary:60J27: Continuous-time Markov processes on discrete state spaces
Secondary:60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 2 , June 1998, pp. 313 - 324
Copyright
Copyright © Applied Probability Trust 1998 

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