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]).
Mots clés : limit theorems for additive functionals, Feynman-Kac functionals, long brownian bridges
@article{PS_2010__14__65_0,
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://www.numdam.org/articles/10.1051/ps:2008028/}
}
TY - JOUR AU - Roynette, Bernard AU - Yor, Marc TI - Local limit theorems for brownian additive functionals and penalisation of brownian paths, IX JO - ESAIM: Probability and Statistics PY - 2010 SP - 65 EP - 92 VL - 14 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2008028/ DO - 10.1051/ps:2008028 LA - en ID - PS_2010__14__65_0 ER -
%0 Journal Article %A Roynette, Bernard %A Yor, Marc %T Local limit theorems for brownian additive functionals and penalisation of brownian paths, IX %J ESAIM: Probability and Statistics %D 2010 %P 65-92 %V 14 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2008028/ %R 10.1051/ps:2008028 %G en %F PS_2010__14__65_0
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. http://www.numdam.org/articles/10.1051/ps:2008028/
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