Measure-valued branching processes with immigration
نویسندگان
چکیده
منابع مشابه
Poisson representations of branching Markov and measure-valued branching processes
Representations of measure-valued processes in terms of countable systems of particles are constructed for models with spatially varying birth and death rates. Each particle has a location and a “level,” but unlike earlier constructions, the levels change with time. In fact, death of a particle occurs only when the level of the particle hits infinity. For each time t the joint distribution of l...
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We consider a particle system in continuous time, discrete population, with spatial motion and nonlocal branching. The offspring’s weights and their number may depend on the mother’s weight. Our setting captures, for instance, the processes indexed by a Galton-Watson tree. Using a size-biased auxiliary process for the empirical measure, we determine this asymptotic behaviour. We also obtain a l...
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Classical super-Brownian motion (SBM) is known to take values in the space of absolutely continuous measures only if d=1. For d¿2 its values are almost surely singular with respect to Lebesgue measure. This result has been generalized to more general motion laws and branching laws (yielding di erent critical dimensions) and also to catalytic SBM. In this paper we study the case of a catalytic m...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1992
ISSN: 0304-4149
DOI: 10.1016/0304-4149(92)90061-t