Sur le temps local d’intersection du mouvement brownien plan et la méthode de rénormalisation de Varadhan. (French) Zbl 0563.60072

le Gall, Jean-François

Sémin. de probabilités XIX, Univ. Strasbourg 1983/84, Proc., Lect. Notes Math. 1123, 314-331 (1985).

[For the entire collection see Zbl 0549.00007.]
A simple construction is given for the local time of self-intersections of Brownian motion in \({\mathbb{R}}^ 2\) or \({\mathbb{R}}^ 3\). This method leads to an easy derivation of S. R. S. Varadhan’s renormalization result for two-dimensional Brownian motion [Appendix to K. Symanzik, Euclidean quantum field theory, in R. Jost (ed.): Local quantum theory, Academic Press (1969)]. The limit variable of Varadhan’s result is also shown to arise in a central limit theorem for the two-dimensional Wiener sausage.

MSC:

60J65	Brownian motion
60G17	Sample path properties

Keywords:

local time of self-intersections; renormalization result; two-dimensional Wiener sausage