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On the Hausdorff measure of multiple points and collision points of super-Brownian motion. (English) Zbl 0857.60045

Summary: We determine the exact Hausdorff measure function of the set of \(k\)-multiple points of super-Brownian motion in dimension \(d>4\). This result was conjectured by D. A. Dawson, I. Iscoe and E. A. Perkins [Probab. Theory Relat. Fields 83, No. 1, 135-205 (1989; Zbl 0692.60063)]. We also give a lower bound, in terms of Hausdorff measure, of the size of the set of collision points of two independent super-Brownian motions. Our proofs make use of the “Brownian snake” introduced by Le Gall.

MSC:

60G57 Random measures
60G17 Sample path properties

Citations:

Zbl 0692.60063
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