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Zbl 1016.60091
Dawson, Donald A.; Fleischmann, Klaus; Mytnik, Leonid; Perkins, Edwin A.; Xiong, Jie
Mutually catalytic branching in the plane: Uniqueness. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 39, No.1, 135-191 (2003). ISSN 0246-0203

Summary: We study a pair of populations in $\bbfR^2$ which undergo diffusion and branching. The system is interactive in that the branching rate of each type is proportional to the local density of the other type. Previous work had established the existence of such a process and derived some of its small scale and large scale properties. This paper is primarily focused on the proof of uniqueness of solutions to the martingale problem associated with the model. The self-duality property of solutions, which is crucial for proving uniqueness and was used in the previous work to derive many of the qualitative properties of the process, is also established.

MSC 2000:: *60K35 Interacting random processes
60G57 Random measures
60J80 Branching processes

Keywords: catalytic super-Brownian motion; collision local time; martingale problem duality; uniqueness; Markov property

Cited in: Zbl 1016.60075

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