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Issue ESAIM: PS
Volume 13, 2009
Page(s) 152 - 180
DOI 10.1051/ps:2008003
Published online 11 June 2009

ESAIM: PS, June 2009, Vol. 13, p. 152-180
DOI: 10.1051/ps:2008003

Penalisations of multidimensional Brownian motion, VI

Bernard Roynette1, Pierre Vallois1 and Marc Yor2, 3

1  Université Henri Poincaré, Institut Elie Cartan, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex, France; Pierre.Vallois@iecn.u-nancy.fr
2  Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 place Jussieu – Case 188, 75252 Paris Cedex 05, France.
3  Institut Universitaire de France, France.


Received July 9, 2007. Revised January 28, 2008. Published online 11 June 2009

Abstract
As in preceding papers in which we studied the limits of penalized 1-dimensional Wiener measures with certain functionals $\Gamma_t$, we obtain here the existence of the limit, as $t\to\infty$, 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 $\geq$ 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.


Mathematics Subject Classification. 60F17, 60F99, 60G44, 60H20, 60J60

Key words: Skew-product decomposition, Brownian windings, Dirichlet problem, spectral decomposition


© EDP Sciences, SMAI 2009


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