MEASURE-VALUED BRANCHING-PROCESSES WITH IMMIGRATION

[摘要] Starting from the cumulant semigroup of a measure-valued branching process, we construct the transition probabilities of some Markov process Y(beta) = (Y(t)(beta), t is-an-element-of R), which we call a measure-valued branching process with discrete immigration of unit beta. The immigration of Y(beta) is governed by a Poisson random measure rho on the time-distribution space and a probability generating function h, both depending on beta. It is shown that, under suitable hypotheses, Y(beta) approximates to a Markov process Y = (Y(t), t is-an-element-of R) as beta --> 0+. The latter is the one we call a measure-valued branching process with immigration. The convergence of branching particle systems with immigration is also studied.

[发布日期] 1992-12-01

[关键词] MEASURE-VALUED BRANCHING PROCESS;IMMIGRATION;PARTICLE SYSTEM;SUPERPROCESS;WEAK CONVERGENCE