Superprocesses with Dependent Spatial Motion and General Branching Densities

Details Superprocesses with Dependent Spatial Motion and General Branching Densities Superprocesses with Dependent Spatial Motion and General Branching Densities

2006-06-24

arxiv.org/abs/math/0606615v1

Electronic Journal of Probability 6 (2001), Paper No. 25, 1-33

Mathematics

Probability

Scientific paper

We construct a class of superprocesses by taking the high density limit of a sequence of interacting-branching particle systems. The spatial motion of the superprocess is determined by a system of interacting diffusions, the branching density is given by an arbitrary bounded non-negative Borel function, and the superprocess is characterized by a martingale problem as a diffusion process with state space $M(\IR)$, improving and extending considerably the construction of Wang (1997, 1998). It is then proved in a special case that a suitable rescaled process of the superprocess converges to the usual super Brownian motion. An extension to measure-valued branching catalysts is also discussed.

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