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Immigration Processes Associated with Branching Particle Systems

Zeng-Hu Li
Advances in Applied Probability
Vol. 30, No. 3 (Sep., 1998), pp. 657-675
Stable URL: http://www.jstor.org/stable/1428144
Page Count: 19
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Immigration Processes Associated with Branching Particle Systems
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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.

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