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Some limit theorems for continuous-state branching processes

Part of: Markov processes

Published online by Cambridge University Press:  09 April 2009

Anthony G Pakes
Anthony G Pakes
Affiliation:
Department of Mathematics University of Western Australia, Nedlands, 6009Western AustraliaAustralia
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Abstract

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The most general continuous time and state branching (C.B.) process (Xt) can be constructed as a certain random time transformation of a spectrally positive Levy process. When the generating process is compound Poisson with a superimposed negative linear drift and the C.B. process is not supercritical, then there is a random time T such that Xt+T = e-ctXT where c > 0 is the drift parameter. Thus T is the last epoch of random variation.

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 44 , Issue 1 , February 1988 , pp. 71 - 87
Copyright
Copyright © Australian Mathematical Society 1988

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