Geodesic
Penalisations of multidimensional brownian motion, VI
Roynette, Bernard  ; Vallois, Pierre  ; Yor, Marc1 
1 Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 place Jussieu – Case 188, 75252 Paris Cedex 05, France.
ESAIM: Probability and Statistics, Tome 13 (2009), pp. 152-180 Cet article a éte moissonné depuis la source Numdam

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As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals Γ t , 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.

DOI : 10.1051/ps:2008003
Classification : 60F17, 60F99, 60G44, 60H20, 60J60
Keywords: skew-product decomposition, brownian windings, Dirichlet problem, spectral decomposition

Roynette, Bernard  ; Vallois, Pierre  ; Yor, Marc 1

1 Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 place Jussieu – Case 188, 75252 Paris Cedex 05, France. 
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Roynette, Bernard; Vallois, Pierre; Yor, Marc. Penalisations of multidimensional brownian motion, VI. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 152-180. doi: 10.1051/ps:2008003

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