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Immigration processes associated with branching particle systems

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Zeng-Hu Li
Zeng-Hu Li*
Affiliation:
Beijing Normal University
*
∗ Postal address: Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China. Email address: lizh@email.bnu.edu.cn
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Abstract

The immigration processes associated with a given branching particle system are formulated by skew convolution semigroups. It is shown that every skew convolution semigroup corresponds uniquely to a locally integrable entrance law for the branching particle system. The immigration particle system may be constructed using a Poisson random measure based on a Markovian measure determined by the entrance law. In the special case where the underlying process is a minimal Brownian motion in a bounded domain, a general representation is given for locally integrable entrance laws for the branching particle system. The convergence of immigration particle systems to measure-valued immigration processes is also studied.

Keywords

Branching particle systemimmigrationDawson-Watanabe superprocessskew convolution semigroupentrance lawminimal Brownian motionconvergence

MSC classification

Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Secondary: 60G57: Random measures
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 30 , Issue 3 , September 1998 , pp. 657 - 675
Copyright
Copyright © Applied Probability Trust 1998 

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Footnotes

Research supported by the National Natural Science Foundation of China (Grant No. 19361060).

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