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State classification for a class of interacting superprocesses with location dependent branching. (English) Zbl 1010.60078
A class of interacting superprocesses on \(\mathbb{R}\) was introduced by D. A. Dawson, Z. Li and the author [Electron. J. Probab. 6, Paper No. 25 (2001; Zbl 1008.60093)]. There it was shown that if the motion coefficient satisfies a uniform ellipticity condition, the process lives in the set of absolutely continuous measures. The main result of the present paper is that in the case of a vanishing motion coefficient, the states are purely atomic, and their dynamics is described.

MSC:
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J35 Transition functions, generators and resolvents
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