Ten penalisation results of Brownian motion involving its one-sided supremum until first and last passage times, VIII

We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before t , respectively first zero after t , of that Brownian motion. This study presents some analogy with penalisation by the longest length of Brownian excursions, up to time t . © 2008 Elsevier Inc. All rights reserved.