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

1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : We penalise Brownian motion by a function of its one-sided supremum considered up to the last zero before $t$, resp. 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 $t$.
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Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-00275170
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Bernard Roynette, Marc Yor. Ten penalisation results of Brownian motion involving its one-sided supremum until first and last passage times, VIII. Journal of Functional Analysis, Elsevier, 2008, 255 (9), pp.2606-2640. ⟨10.1016/j.jfa.2008.04.024⟩. ⟨hal-00275170⟩

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