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2001 Superprocesses with Dependent Spatial Motion and General Branching Densities
Donald Dawson, Zenghu Li, Hao Wang
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Electron. J. Probab. 6: 1-33 (2001). DOI: 10.1214/EJP.v6-98


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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Donald Dawson. Zenghu Li. Hao Wang. "Superprocesses with Dependent Spatial Motion and General Branching Densities." Electron. J. Probab. 6 1 - 33, 2001.


Accepted: 25 May 2001; Published: 2001
First available in Project Euclid: 19 April 2016

zbMATH: 1008.60093
MathSciNet: MR1873302
Digital Object Identifier: 10.1214/EJP.v6-98

Primary: 60G57 , 60J80
Secondary: 60J35

Keywords: diffusion process , Dual process , interacting-branching particle system , Martingale problem , measure-valued catalyst , rescaled limit , Superprocess


Vol.6 • 2001
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