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]).
Keywords: 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},
year = {2010},
publisher = {EDP Sciences},
volume = {14},
doi = {10.1051/ps:2008028},
mrnumber = {2654548},
language = {en},
url = {https://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 - https://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 https://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
[1] , An introduction to probability theory and its applications, volume II. John Wiley & Sons Inc., New York (1966). | Zbl
[2] and , Limiting distributions associated with moments of exponential Brownian functionals. Studia Sci. Math. Hung. 41 (2004) 193-242. | Zbl
[3] , Semimartingales et grossissement d'une filtration. Lect. Notes Maths 833. Springer (1980). | Zbl
[4] and , Eds., Grossissements de filtrations: exemples et applications. Lect. Notes Maths 1118. Springer (1985). | Zbl
[5] and , Brownian motion and Stochastic Calculus. Springer (1991). | Zbl
[6] , Asymptotics for expectations of multiplicative functionals of 1-dimensional Brownian motion. Preprint (2006).
[7] , Special functions and their applications. Dover (1972). | Zbl
[8] and , Random Times and Enlargement of Filtrations in a Brownian Setting. Lect. Notes Maths 1873. Springer (2006). | Zbl
[9] , and , A global view of Brownian penalisations. MSJ Memoirs, volume 19. Mathematical Society of Japan, Tokyo (2009). | Zbl
[10] and , Continuous Martingales and Brownian Motion. Third edition. Springer (1999). | Zbl
[11] and , Penalising Brownian paths. Lect. Notes Maths 1969. Springer (2009). | Zbl
[12] , and , Penalisation of a Brownian motion with drift by a function of its one-sided maximum and its position, III. Periodica Math. Hung. 50 (2005) 247-280. | Zbl
[13] , and , Some penalisations of the Wiener measure. Japan J. Math. 1 (2006) 263-299. | Zbl
[14] , and , Limiting laws associated with Brownian motion perturbed by normalized exponential weights. Studia Sci. Math. Hung. 43 (2006) 171-246. | Zbl
[15] , and , Limiting laws associated with Brownian motions perturbed by its maximum, minimum, and local time, II. Studia Sci. Math. Hung. 43 (2006) 295-360. | Zbl
[16] , The distribution of Brownian quantiles. J. Appl. Prob. 32 (1995) 405-416. | Zbl
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