Le cocycle brownien de degré deux comme bruit blanc sur les droites affines de l'espace

Abstract

Inspired by the work of Čencov [N.N. Čencov, Le mouvement brownien à plusieurs paramètres de M. Lévy et le bruit blanc généralisé, Teor. Veroyatnost. i Primenen. 3 (1957) 281–282. [1]] on multiparameter Lévy's Brownian motion (see [P. Lévy, Processus Stochastiques et Mouvement Brownien. Suivi d'une note de M. Loève, Gauthier-Villars, Paris, 1948. [4]]), we show that the white noise on the straight lines in dimension three generates a cocycle of degree two, whose restrictions to plans have the law of plane Brownian sheets. We check that this degree two cocycle is the same than the one studied by us in a preceding work. Consequently we give here another proof of the existence of the degree two Brownian cocycle in dimension three. Moreover this construction is adapted to the numerical simulation. To cite this article: J. Depauw, C. R. Acad. Sci. Paris, Ser. I 342 (2006).