Measure-valued branching processes with immigration

Zeng-Hu Li

Stochastic Processes and their Applications, 1992, vol. 43, issue 2, 249-264

Abstract: Starting from the cumulant semigroup of a measure-valued branching process, we construct the transition probabilities of some Markov process Y([beta])=(Y([beta])t, t [epsilon] , 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=(Yt, t [epsilon] 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.

Keywords: measure-valued; branching; process; immigration; particle; system; superprocess; weak; convergence (search for similar items in EconPapers)
Date: 1992
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Citations: View citations in EconPapers (7)

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