State classification for a class of interacting superprocesses with location dependent branching (Q1860593)
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scientific article; zbMATH DE number 1873767
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | State classification for a class of interacting superprocesses with location dependent branching |
scientific article; zbMATH DE number 1873767 |
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State classification for a class of interacting superprocesses with location dependent branching (English)
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25 February 2003
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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.
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purely atomic states
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uniform ellipticity condition
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vanishing motion coefficient
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