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

✍ Scribed by J. F. Gall; M. Yor

• Book ID: 104740539
• Publisher: Springer
• Year: 1987
• Tongue: English
• Weight: 834 KB
• Volume: 74
• Category: Article
• ISSN: 1432-2064
• DOI: 10.1007/bf00363519

✦ Synopsis

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,.--, Pk, k planes which intersect two by two. Then, the convergences in distribution concerning the planar Brownian motions B i (l<i<k), defined respectively as the orthogonal projections of B on P~ (l<i<k), take place jointly, and the corresponding limit variables are independent.