Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time II

Bernard Roynette (1, 2) , Pierre P. Vallois (1, 2) , Marc Yor (3)

1 IECN - Institut Élie Cartan de Nancy
2 OMEGA - Probabilistic numerical methods
3 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We obtain probability measures on the canonical space penalizing the Wiener measure by a function of its maximum (resp. minimum, local time). We study the law of the canonical process under these new probability measures.

Domaines: Probabilités [math.PR]

Bernard Roynette, Pierre P. Vallois, Marc Yor. Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time II. Studia Scientiarum Mathematicarum Hungarica, 2006, 43 (3), pp.295-360. ⟨hal-00012705⟩