Immigration processes associated with branching particle systems
1998 ◽
Vol 30
(3)
◽
pp. 657-675
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Keyword(s):
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
(03)
◽
pp. 657-675
◽
2007 ◽
Vol 10
(03)
◽
pp. 439-464
◽
2009 ◽
Vol 12
(04)
◽
pp. 593-612
◽
1991 ◽
Vol 43
(5)
◽
pp. 985-997
◽
1994 ◽
Vol 37
(2)
◽
pp. 187-196
◽
Keyword(s):