Brownian penalisations related to excursion lengths, VII
Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 2, pp. 421-452.

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.

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.

DOI: 10.1214/08-AIHP177
Classification: 60F17,  60F99,  60G17,  60G40,  60G44,  60H10,  60H20,  60J25,  60J55,  60J60,  60J65
Keywords: longest length of excursions, brownian meander, penalisation
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Roynette, B.; Vallois, P.; Yor, M. Brownian penalisations related to excursion lengths, VII. Annales de l'I.H.P. Probabilités et statistiques, Volume 45 (2009) no. 2, pp. 421-452. doi : 10.1214/08-AIHP177. http://www.numdam.org/articles/10.1214/08-AIHP177/

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