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Asymptotic Behaviour of Continuous Time and State Branching Processes

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  09 April 2009

Zeng-Hu Li
Zeng-Hu Li
Affiliation:
Department of Mathematics Beijing Normal UniversityBeijing 100875 P. R.China e-mail: lizh@email.bun.edu.cn
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Abstract

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We prove some limit theorems for contiunous time and state branching processes. The non-degenerate limit laws are obtained in critical and non-critical cases by conditioning or introducing immigration processes. The limit laws in non-critical cases are characterized in terms of the cononical measure of the cumulant semigroup. The proofs are based on estimates of the cumulant semigroup derived from the forward and backward equations, which are easier than the proffs in the classical setting.

Keywords

branching processescontinuous timecontinuous sateconditioningimmigrationlimit theorem

MSC classification

Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60F05: Central limit and other weak theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 1 , February 2000 , pp. 68 - 84
Copyright
Copyright © Australian Mathematical Society 2000

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