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Nonidentifiability of the Two-State Markovian Arrival Process

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Pepa Ramírez-Cobo ,
Rosa E. Lillo  and
Michael P. Wiper
Pepa Ramírez-Cobo*
Affiliation:
CNRS
Rosa E. Lillo*
Affiliation:
Universidad Carlos III de Madrid
Michael P. Wiper*
Affiliation:
Universidad Carlos III de Madrid
*
∗Current address: Instituto Universitario de Matemáticas de la Universidad de Sevilla (IMUS), Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes, s/n, 41012 Sevilla, Spain. Email address: [email protected]
∗∗Postal address: Departamento de Estadística, Universidad Carlos III. C/ Madrid, 126 – 28903 Getafe (Madrid), Spain.
∗∗Postal address: Departamento de Estadística, Universidad Carlos III. C/ Madrid, 126 – 28903 Getafe (Madrid), Spain.
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Abstract

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In this paper we consider the problem of identifiability for the two-state Markovian arrival process (MAP2). In particular, we show that the MAP2 is not identifiable, providing the conditions under which two different sets of parameters induce identical stationary laws for the observable process.

Keywords

Markovian arrival processMarkov-modulated Poisson processphase-type renewal processidentifiability problem

MSC classification

Secondary: 60G55: Point processes 60J05: Discrete-time Markov processes on general state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 3 , September 2010 , pp. 630 - 649
Copyright
Copyright © Applied Probability Trust 2010 

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