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

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.


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


Zbl 1008.60093
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