Il est prouvé que les lois limites, lorsque t→∞, du mouvement brownien pénalisé par la plus grande longueur des excursions jusqu'en t, ou bien jusqu'au dernier zéro avant t, ou encore jusqu'au premier zéro après t, existent. Ces lois limites sont décrites en détail.
Limiting laws, as t→∞, for brownian motion penalised by the longest length of excursions up to t, or up to the last zero before t, or again, up to the first zero after t, are shown to exist, and are characterized.
Mots-clés : longest length of excursions, brownian meander, penalisation
@article{AIHPB_2009__45_2_421_0, author = {Roynette, B. and Vallois, P. and Yor, M.}, title = {Brownian penalisations related to excursion lengths, {VII}}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {421--452}, publisher = {Gauthier-Villars}, volume = {45}, number = {2}, year = {2009}, doi = {10.1214/08-AIHP177}, mrnumber = {2521408}, zbl = {1181.60046}, language = {en}, url = {http://archive.numdam.org/articles/10.1214/08-AIHP177/} }
TY - JOUR AU - Roynette, B. AU - Vallois, P. AU - Yor, M. TI - Brownian penalisations related to excursion lengths, VII JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2009 SP - 421 EP - 452 VL - 45 IS - 2 PB - Gauthier-Villars UR - http://archive.numdam.org/articles/10.1214/08-AIHP177/ DO - 10.1214/08-AIHP177 LA - en ID - AIHPB_2009__45_2_421_0 ER -
%0 Journal Article %A Roynette, B. %A Vallois, P. %A Yor, M. %T Brownian penalisations related to excursion lengths, VII %J Annales de l'I.H.P. Probabilités et statistiques %D 2009 %P 421-452 %V 45 %N 2 %I Gauthier-Villars %U http://archive.numdam.org/articles/10.1214/08-AIHP177/ %R 10.1214/08-AIHP177 %G en %F AIHPB_2009__45_2_421_0
Roynette, B.; Vallois, P.; Yor, M. Brownian penalisations related to excursion lengths, VII. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 2, pp. 421-452. doi : 10.1214/08-AIHP177. http://archive.numdam.org/articles/10.1214/08-AIHP177/
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