Penalisations of multidimensional Brownian motion, VI

Bernard Roynette (1) , Pierre P. Vallois (2, 1) , Marc Yor (3, 4)

1 IECN - Institut Élie Cartan de Nancy
2 BIGS - Biology, genetics and statistics
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
4 IUF - Institut universitaire de France

As in preceding papers in which we studied the limits of penalized one-dimensional Wiener measures with certain functionals Γt, we obtain here the existence of the limit, as t → ∞, of d-dimensional Wiener measures penalized by a function of the maximum up to time t of the Brownian winding process (for d = 2), or in d ≥ 2 dimensions for Brownian motion prevented to exit a cone before time t. Various extensions of these multidimensional penalisations are studied, and the limit laws are described. Throughout this paper, the skew-product decomposition of d-dimensional Brownian motion plays an important role.

Mots clés: Skew-product decomposition; Brownian windings; Dirichlet problem; spectral decomposition

Domaines: Probabilités [math.PR]

Bernard Roynette, Pierre P. Vallois, Marc Yor. Penalisations of multidimensional Brownian motion, VI. ESAIM: Probability and Statistics, 2009, 13, pp.152-180. ⟨10.1051/ps:2008003⟩. ⟨hal-00591324⟩