skew convolution semigroup
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1998 ◽  
Vol 30 (03) ◽  
pp. 657-675 ◽  
Author(s):  
Zeng-Hu Li

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.


1998 ◽  
Vol 30 (3) ◽  
pp. 657-675 ◽  
Author(s):  
Zeng-Hu Li

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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