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An extended class of time-continuous branching processes

Part of:Markov processes

Published online by Cambridge University Press:  14 July 2016

Rong-Rong Chen
Rong-Rong Chen*
Affiliation:
University of Illinois at Urbana-Champaign
*
∗ Postal address: Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
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Abstract

This paper is devoted to studying an extended class of time-continuous branching processes, motivated by the study of stochastic control theory and interacting particle systems. The uniqueness, extinction, recurrence and positive recurrence criteria for the processes are presented. The main new point in our proofs is the use of several different comparison methods. The resulting picture shows that the methods are effective and hence should also be meaningful in other situations.

Keywords

BRANCHING PROCESSESUNIQUENESSRECURRENCEPOSITIVE RECURRENCE

MSC classification

Primary:60J80: Branching processes (Galton-Watson, birth-and-death, etc.)60J85: Applications of branching processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997, pp. 14 - 23
Copyright
Copyright © Applied Probability Trust 1997 

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