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A generic property of phase-type representations

Part of: Statistics Markov processes

Published online by Cambridge University Press:  14 July 2016

Christian Commault  and
Stéphane Mocanu
Christian Commault*
Affiliation:
Laboratoire d’Automatique de Grenoble
Stéphane Mocanu*
Affiliation:
Laboratoire d’Automatique de Grenoble
*
∗ Postal address: Laboratoire d’Automatique de Grenoble UMR 5528, INPG-CNRS-UJF, ENSIEG, BP 46, 38402 Saint Martin d’Hères Cedex, France.
∗ Postal address: Laboratoire d’Automatique de Grenoble UMR 5528, INPG-CNRS-UJF, ENSIEG, BP 46, 38402 Saint Martin d’Hères Cedex, France.
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Abstract

In this paper we introduce the notion of structured phase-type representations. A structured representation corresponds to a class of phase-type representations having the same graph but free parameters. We define a generic property for such a representation. Then we prove that, generically, an irreducible structured representation of a given order corresponds to a distribution whose degree is equal to this order.

Keywords

Markov chainsphase-type distributionsphase-type representationsgeneric order

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 62-09: Graphical methods
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 775 - 785
Copyright
Copyright © Applied Probability Trust 2002 

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