Summary.
The spatial structure of a new class of measure-valued diffusions which arise as limits in distribution of a sequence of interacting branching particle systems is investigated. We obtain the following criterion of state classification for these superprocesses: their effective state space is contained in the set of purely atomic measures or the set of absolutely continuous measures according as ε=0 or ε≠0, when the coefficient of the motion generator is a smooth function.
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Received: 15 December 1995 / In revised form: 24 March 1997
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Wang, H. State classification for a class of measure-valued branching diffusions in a Brownian medium. Probab Theory Relat Fields 109, 39–55 (1997). https://doi.org/10.1007/s004400050124
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DOI: https://doi.org/10.1007/s004400050124
- Key words and phrases: spatial structure
- property
- superprocess
- interaction.
- Mathematics Subject Classification (1991): 60K35
- 60J80
- 60J35