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

Serlet, Laurent

Stochastics Stochastics Rep. 54, No. 3-4, 169-198 (1995).

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

Keywords:

super-Brownian motion; Hausdorff measure; Brownian snake; multiple points; collision points; tree structure; additive functionals

Citations:

Zbl 0692.60063