Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace

Summary The existence of a joint asymptotic distribution for the windings of a three-dimensional Brownian motion around a finite number of straight lines is obtained. This complements the recent studies, by Pitman- Yor, and the authors, of the joint asymptotic distribution for the windings of planar Brownian motion around a finite number of points.The following principle governs the passage from results in the plane to results in space:Let B be a three-dimensional Brownian motion, and P₁, ..., P_k, k planes which intersect two by two. Then, the convergences in distribution concerning the planar Brownian motions Bⁱ (1ik), defined respectively as the orthogonal projections of B on P_i (1ik), take place jointly, and the corresponding limit variables are independent.