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.
@article{1241024675,
author = {Roynette, B. and Vallois, P. and Yor, M.},
title = {Brownian penalisations related to excursion lengths, VII},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {45},
number = {1},
year = {2009},
pages = { 421-452},
language = {en},
url = {http://dml.mathdoc.fr/item/1241024675}
}
Roynette, B.; Vallois, P.; Yor, M. Brownian penalisations related to excursion lengths, VII. Ann. Inst. H. Poincaré Probab. Statist., Tome 45 (2009) no. 1, pp. 421-452. http://gdmltest.u-ga.fr/item/1241024675/