| Issue |
ESAIM: PS
Volume 14, 2010
|
|
|---|---|---|
| Page(s) | 65 - 92 | |
| DOI | https://doi.org/10.1051/ps:2008028 | |
| Published online | 26 March 2010 | |
Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX
1
Institut Elie Cartan, Université Henri Poincaré, BP 239, 54506 Vandoeuvre-lés-Nancy Cedex, France
2
Laboratoire de Probabilités et Modèles Aléatoires, Université Paris VI et VII, 4 place Jussieu, Case 188, 75252 Paris Cedex 05, France
3
Institut Universitaire de France, Paris, France
Corresponding author: Bernard.Roynette@iecn.u-nancy.fr
Received:
17
March
2008
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: 
. 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 [B. Roynette, P. Vallois and M. Yor, Studia Sci. Math. Hung. 43 (2006) 171–246]).
Mathematics Subject Classification: 60F17 / 60G44 / 60J25 / 60J35 / 60J55 / 60J57 / 60J60 / 60J65.
Key words: Limit theorems for additive functionals / Feynman-Kac functionals / long Brownian bridges.
© EDP Sciences, SMAI, 2010
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