Two examples of functional penalisations of Brownian motion, VIII

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

1 IECN - Institut Élie Cartan de Nancy
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 IUF - Institut universitaire de France

On one hand, we penalise Brownian paths by a function of one-sided supremum of Brownian motion, considered up to the last, resp. the first, zero, before $t$, resp. after $t$. This study provides some analogy with penalisations by the longest length of Brownian excursions, up to time $t$. On the other hand, we describe Feynman-Kac type penalisation results for long Brownian bridges, thus completing some similar study for free Brownian motion.

Mots clés: pénalisation of Brownian paths; one-sided supremum; Feynman-Kac functionals; long Brownian bridges

Domaines: Probabilités [math.PR]

Bernard Roynette, Marc Yor. Two examples of functional penalisations of Brownian motion, VIII. 2007. ⟨hal-00139183⟩