Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX

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

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

We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional : $\Big(A_t^{-} := \int_0^t 1_{X_s < 0}ds, t\geq 0\Big) $. On the other hand, we describe Feynman-Kac type penalisation results for long Brownian bridges thus completing some similar previous study for standard Brownian motion (see [RVY,I]).

Mots clés: Limit theorems for additive functionals; Feynman-Kac functionals; long Brownian bridges

Domaines: Probabilités [math.PR]

Bernard Roynette, Marc Yor. Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX. 2008. ⟨hal-00257593⟩