Superprocesses with dependent spatial motion and general branching densities. (English) Zbl 1008.60093

Dawson, Donald A.; Li, Zenghu; Wang, Hao

Electron. J. Probab. 6, Paper No. 25, 33 p. (2001).

Summary: 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 \(M(R)\), 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.

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60J35	Transition functions, generators and resolvents
60G57	Random measures

Keywords:

superprocess; interacting-branching particle system; diffusion process; martingale problem; dual process; rescaled limit; measure-valued catalyst