Limiting laws associated with Brownian motion perturbated by normalized exponential weights I.

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 determine the rate of decay of the expectation Z(t) of some multiplicative functional related to Brownian motion up to time t. This permits to prove that the Wiener measure, penalized by this multiplicative functional, converges as t goes to infinity to a probability measure (p.m.) . We obtain the law of the canonical process under this new p.m.

Mots clés: normalized exponential weights; Sturm-Liouville equation; Ray-Knight's theorems; rate of convergence; Bessel processes; normalized exponential weights

Domaines: Probabilités [math.PR]

Bernard Roynette, Pierre P. Vallois, Marc Yor. Limiting laws associated with Brownian motion perturbated by normalized exponential weights I.. Studia Scientiarum Mathematicarum Hungarica, 2006, 43 (2), pp.171-246. ⟨hal-00012523⟩