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GENERALIZED CLASS [Cscr ] MARKOV CHAINS AND COMPUTATION OF CLOSED-FORM BOUNDING DISTRIBUTIONS

Published online by Cambridge University Press:  27 February 2007

Mouad Ben Mamoun ,
Ana Bušić  and
Nihal Pekergin
Mouad Ben Mamoun
Affiliation:
PRiSM, Université Versailles St Quentin, 78035 Versailles, France, and, Université Mohammed V, Rabat, Maroc
Ana Bušić
Affiliation:
PRiSM, Université Versailles St Quentin, 78035 Versailles, France
Nihal Pekergin
Affiliation:
PRiSM, Université Versailles St Quentin, 78035 Versailles, France, and, Centre Marin Mersenne, Université Paris 1, 75013 Paris, France, E-mail: {mobe,abusic,nih}@prism.uvsq.fr
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Abstract

In this article we first give a characterization of a class of probability transition matrices having closed-form solutions for transient distributions and the steady-state distribution. We propose to apply the stochastic comparison approach to construct bounding chains belonging to this class. Therefore, bounding chains can be analyzed efficiently through closed-form solutions in order to provide bounds on the distributions of the considered Markov chain. We present algorithms to construct upper-bounding matrices in the sense of the ≤st and ≤icx order.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 21 , Issue 2 , April 2007 , pp. 235 - 260
Copyright
© 2007 Cambridge University Press

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References

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