State classification for a class of interacting superprocesses with location dependent branching
A class of interacting superprocesses on \(\mathbb{R}\) was introduced by \textit{D. A. Dawson}, \textit{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.
scientific article; zbMATH DE number 1873767