Penalisations of multidimensional brownian motion, VI

Roynette, Bernard; Vallois, Pierre; Yor, Marc

doi:10.1051/ps:2008003

Geodesic

Parcourir par

Penalisations of multidimensional brownian motion, VI

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.

ESAIM: Probability and Statistics, Tome 13 (2009), pp. 152-180

Voir la notice de l'article provenant de la source Numdam

Résumé

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 $t \to \infty$ , 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.

DOI : 10.1051/ps:2008003

Classification : 60F17, 60F99, 60G44, 60H20, 60J60
Keywords: skew-product decomposition, brownian windings, Dirichlet problem, spectral decomposition

Affiliations des auteurs :

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.

@article{PS_2009__13__152_0,
     author = {Roynette, Bernard and Vallois, Pierre and Yor, Marc},
     title = {Penalisations of multidimensional brownian motion, {VI}},
     journal = {ESAIM: Probability and Statistics},
     pages = {152--180},
     publisher = {EDP-Sciences},
     volume = {13},
     year = {2009},
     doi = {10.1051/ps:2008003},
     mrnumber = {2518544},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2008003/}
}

TY  - JOUR
AU  - Roynette, Bernard
AU  - Vallois, Pierre
AU  - Yor, Marc
TI  - Penalisations of multidimensional brownian motion, VI
JO  - ESAIM: Probability and Statistics
PY  - 2009
SP  - 152
EP  - 180
VL  - 13
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps:2008003/
DO  - 10.1051/ps:2008003
LA  - en
ID  - PS_2009__13__152_0
ER  -

%0 Journal Article
%A Roynette, Bernard
%A Vallois, Pierre
%A Yor, Marc
%T Penalisations of multidimensional brownian motion, VI
%J ESAIM: Probability and Statistics
%D 2009
%P 152-180
%V 13
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps:2008003/
%R 10.1051/ps:2008003
%G en
%F PS_2009__13__152_0

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

Cité par Sources :