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

**Donald A. Dawson**

*(Carleton University)*

**Zenghu Li**

*(Beijing Normal University)*

**Hao Wang**

*(University of Oregon)*

#### Abstract

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 $M({\bf R})$, 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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Pages: 1-33

Publication Date: May 25, 2001

DOI: 10.1214/EJP.v6-98

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