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| HAL : hal-00104923, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Two studies of penalisations of Brownian path : VI Penalisations of multidimensional Brownian motion VII Brownian penalisations related to excursion lengths |
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| Bernard Roynette 1Pierre P. Vallois 1 |
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| (2007) |
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| In the same vein as in preceding papers in which we studied the limits of penalized one-dimensional Wiener measures with certain functionals $\Gamma_t$, we obtain here the existence of the limit, as $t \longrightarrow \infty$, 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. Limiting laws, as $t \longrightarrow \infty$, for Brownian motion penalised by the longest length of excursions up to $t$, or up to the last zero before $t$, or agai, up to the first zero after $t$, are shown to exist, and are characterized. |
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| 1 : | Institut Elie Cartan Nancy (IECN) |
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CNRS : UMR7502 – INRIA – Université Henri Poincaré - Nancy I – Université Nancy II – Institut National Polytechnique de Lorraine (INPL) |
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| 2 : | Laboratoire de Probabilités et Modèles Aléatoires (LPMA) |
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CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot |
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| 3 : | Institut Universitaire de France (IUF) |
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Ministère de l'Enseignement Supérieur et de la Recherche Scientifique |
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| Domaine | : | Mathématiques/Probabilités |
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| Skew-product decomposition – Brownian windings – Dirichlet problem – spectral decomposition – longest length of excursions – Brownian meander – penalisation |
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| hal-00104923, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00104923 | |
| oai:hal.archives-ouvertes.fr:hal-00104923 | |
| Contributeur : Pierre Vallois | |
| Soumis le : Lundi 9 Octobre 2006, 17:18:55 | |
| Dernière modification le : Lundi 9 Octobre 2006, 17:18:55 | |
