Superprocesses with coalescing Brownian spatial motion as large-scale limits. (English) Zbl 1067.60085

Dawson, D. A.; Li, Z.; Zhou, X.

J. Theor. Probab. 17, No. 3, 673-692 (2004).

Superprocesses of several types have been shown to arise as limits of various kinds of branching and interacting particle systems. A class of superprocesses with dependent spatial motion (SDSM) has been studied by several authors. In particular, D. A. Dawson, Z. Li and H. Wang [Electron. J. Probab. 6, Paper No. 25 (2001; Zbl 1008.60093)] stated that in the case of the purely atomic SDSM studied therein, a suitably rescaled limit would lead to a superprocess with coalescing spatial motion (SCSM), which seems to be a new phenomenon in this area, but this was not proved because some questions regarding the SCSM remained open. In this paper the above-mentioned statement is proved. The proof is based on one-dimensional excursions.

Reviewer: Louis G. Gorostiza (Mexico City)

MSC:

60J80	Branching processes (Galton-Watson, birth-and-death, etc.)
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
60G57	Random measures
60K35	Interacting random processes; statistical mechanics type models; percolation theory

Keywords:

coalescing spatial motion; excursions; scaling limit; Poisson random measure

Citations:

Zbl 1008.60093