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Interacting measure branching processes. Some bounds for the support. (English) Zbl 0786.60065
The measure branching processes are introduced to describe branching and diffusing particles. There are considered the models of high branching rate for particles with small masses. According to such renormalization there are derived the limit theorems with the limit point $$X$$, interacting measure branching process, that is a continuous square- integrable real martingale. Further it is proved that $$X$$ is a solution of a general stochastic differential equation in a space of vector measures. In the last part particular cases are considered. In a first example it is computed a lower bound for the Hausdorff dimension of the support of an interacting measure branching process. And in a more particular case the exact Hausdorff dimension is given by using a Girsanov theorem with respect to the law of a noninteracting measure branching process.

MSC:
 60G57 Random measures 60K35 Interacting random processes; statistical mechanics type models; percolation theory 60G44 Martingales with continuous parameter
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