A superprocess involving both branching and coalescing. (English) Zbl 1126.60086

Zhou, Xiaowen

Ann. Inst. Henri Poincaré, Probab. Stat. 43, No. 5, 599-618 (2007).

Summary: We consider a superprocess with coalescing Brownian spatial motion. We first point out a dual relationship between two systems of coalescing Brownian motions. In consequence we can express the Laplace functionals for the superprocess in terms of coalescing Brownian motions, which allows us to obtain some explicit results. We also point out several connections between such a superprocess and the Arratia flow. A more general model is discussed at the end of this paper.

MSC:

60K35	Interacting random processes; statistical mechanics type models; percolation theory
60G57	Random measures
60J65	Brownian motion
60J80	Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

coalescing simple random walk; coalescing Brownian motion; duality; superprocess with coalescing Brownian spatial motion; arratia flow; Laplace functional; Feller’s branching diffusion; Bessel process