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A MARKOV-MODULATED GROWTH COLLAPSE MODEL

Published online by Cambridge University Press:  21 December 2009

Offer Kella  and
Andreas Löpker
Offer Kella
Affiliation:
Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905; Israel E-mail: [email protected]
Andreas Löpker
Affiliation:
EURANDOM and Eindhoven University of Technology, P.O. Box 513; 5600 MB Eindhoven, The Netherlands E-mail: [email protected]
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Abstract

We consider a growth collapse model in a random environment for which the input rates might depend on the state of an underlying irreducible Markov chain and at state change epochs there is a possible downward jump to a level that is a random fraction of the level just before the jump. The distributions of these jumps are allowed to depend on both the originating and target states. Under a very weak assumption we develop an explicit formula for the conditional moments (of all orders) of the time stationary distribution. We then consider special cases and show how to use this result to study a growth collapse process in which the times between collapses have a phase-type distribution.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 1 , January 2010 , pp. 99 - 107
Copyright
Copyright © Cambridge University Press 2009

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