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Penalisations of multidimensional Brownian motion, VI

Published online by Cambridge University Press:  11 June 2009

Bernard Roynette ,
Pierre Vallois  and
Marc Yor
Bernard Roynette
Affiliation:
Université Henri Poincaré, Institut Elie Cartan, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex, France; Pierre.Vallois@iecn.u-nancy.fr
Pierre Vallois
Affiliation:
Université Henri Poincaré, Institut Elie Cartan, BP 239, 54506 Vandoeuvre-lès-Nancy Cedex, France; Pierre.Vallois@iecn.u-nancy.fr
Marc Yor
Affiliation:
Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 place Jussieu – Case 188, 75252 Paris Cedex 05, France. Institut Universitaire de France, France.
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Abstract

As in preceding papers inwhich we studied the limits of penalized 1-dimensional Wienermeasures with certain functionals Γt, we obtain here theexistence of the limit, as t → ∞, of d-dimensional Wienermeasures penalized by a function of the maximum up to time t ofthe Brownian winding process (for d = 2), or in {d}≥ 2dimensions for Brownian motionprevented to exit a cone before time t. Various extensions of these multidimensional penalisations arestudied, and the limit laws are described. Throughout this paper, the skew-product decomposition ofd-dimensional Brownian motion plays an important role.

Keywords

Skew-productdecompositionBrownian windingsDirichlet problemspectraldecomposition
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 13 , July 2009 , pp. 152 - 180
Copyright
© EDP Sciences, SMAI, 2009

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