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

Bernard Roynette (1, 2) , Marc Yor (3)

1 TOSCA - Simuler et calibrer des modèles stochastiques
2 IECN - Institut Élie Cartan de Nancy
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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 $t$.

Mots clés: Penalisations of Brownian paths; one-sided supremum; last and first zeroes before and after a fixed time $t$

Domaines: Probabilités [math.PR]

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, 2008, 255 (9), pp.2606-2640. ⟨10.1016/j.jfa.2008.04.024⟩. ⟨hal-00275170⟩