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

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.)
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