Geodesic
Local limit theorems for brownian additive functionals and penalisation of brownian paths, IX
ESAIM: Probability and Statistics, Tome 14 (2010), pp. 65-92

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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: (A t - :=∫ 0 t 1 X s <0 ds,t≥0). 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]).

DOI : 10.1051/ps:2008028
Classification : 60F17, 60G44, 60J25, 60J35, 60J55, 60J57, 60J60, 60J65
Keywords: limit theorems for additive functionals, Feynman-Kac functionals, long brownian bridges 
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     author = {Roynette, Bernard and Yor, Marc},
     title = {Local limit theorems for brownian additive functionals and penalisation of brownian paths, {IX}},
     journal = {ESAIM: Probability and Statistics},
     pages = {65--92},
     publisher = {EDP-Sciences},
     volume = {14},
     year = {2010},
     doi = {10.1051/ps:2008028},
     mrnumber = {2654548},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps:2008028/}
}
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Roynette, Bernard; Yor, Marc. Local limit theorems for brownian additive functionals and penalisation of brownian paths, IX. ESAIM: Probability and Statistics, Tome 14 (2010), pp. 65-92. doi: 10.1051/ps:2008028

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