[Une mesure σ-finie sur liée à de nombreuses pénalisations browniennes]
Dans cette Note, nous étudions une mesure σ-finie sur l'espace , fortement liée à la mesure de Wiener, et nous construisons une grande classe de martingales browniennes à partir de . Certaines de ces martingales apparaissent naturellement dans l'étude des pénalisations browniennes faite par B. Roynette, P. Vallois et M. Yor.
In this Note, we study a σ-finite measure on the space , strongly related to Wiener measure, and we construct a large class of Brownian martingales from . Some of these martingales appear naturally in the study of Brownian penalisations made by B. Roynette, P. Vallois and M. Yor.
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@article{CRMATH_2007__345_8_459_0,
author = {Najnudel, Joseph and Roynette, Bernard and Yor, Marc},
title = {A remarkable \protect\emph{\ensuremath{\sigma}}-finite measure on $ \mathcal{C}({\mathbf{R}}_{+},\mathbf{R})$ related to many {Brownian} penalisations},
journal = {Comptes Rendus. Math\'ematique},
pages = {459--466},
publisher = {Elsevier},
volume = {345},
number = {8},
year = {2007},
doi = {10.1016/j.crma.2007.09.015},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.09.015/}
}
TY - JOUR
AU - Najnudel, Joseph
AU - Roynette, Bernard
AU - Yor, Marc
TI - A remarkable σ-finite measure on $ \mathcal{C}({\mathbf{R}}_{+},\mathbf{R})$ related to many Brownian penalisations
JO - Comptes Rendus. Mathématique
PY - 2007
SP - 459
EP - 466
VL - 345
IS - 8
PB - Elsevier
UR - http://www.numdam.org/articles/10.1016/j.crma.2007.09.015/
DO - 10.1016/j.crma.2007.09.015
LA - en
ID - CRMATH_2007__345_8_459_0
ER -
%0 Journal Article
%A Najnudel, Joseph
%A Roynette, Bernard
%A Yor, Marc
%T A remarkable σ-finite measure on $ \mathcal{C}({\mathbf{R}}_{+},\mathbf{R})$ related to many Brownian penalisations
%J Comptes Rendus. Mathématique
%D 2007
%P 459-466
%V 345
%N 8
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2007.09.015/
%R 10.1016/j.crma.2007.09.015
%G en
%F CRMATH_2007__345_8_459_0
Najnudel, Joseph; Roynette, Bernard; Yor, Marc. A remarkable σ-finite measure on $ \mathcal{C}({\mathbf{R}}_{+},\mathbf{R})$ related to many Brownian penalisations. Comptes Rendus. Mathématique, Tome 345 (2007) no. 8, pp. 459-466. doi : 10.1016/j.crma.2007.09.015. http://www.numdam.org/articles/10.1016/j.crma.2007.09.015/
[1] Valeurs principales associées aux temps locaux browniens, Bull. Sci. Math. (2), Volume 111 (1987) no. 1, pp. 23-101
[2] J. Najnudel, Temps locaux et pénalisations browniennes, PhD thesis, Université Paris VI, 2007
[3] J. Najnudel, B. Roynette, M. Yor, On a remarkable σ-finite measure W on path space, which rules penalisations for a linear Brownian motion, 2007, in preparation
[4] Continuous martingales and Brownian motion, Grundlehren der Mathematischen Wissenschaften, Fundamental Principles of Mathematical Sciences, vol. 293, Springer-Verlag, Berlin, 1999, pp. 493-511
[5] Limiting laws associated with Brownian motion perturbated by normalized exponential weights, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 337 (2003) no. 10, pp. 667-673
[6] Limiting laws for long Brownian bridges perturbed by their one-sided maximum. III, Period. Math. Hungar., Volume 50 (2005) no. 1–2, pp. 247-280
[7] Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time. II, Studia Sci. Math. Hungar., Volume 43 (2006) no. 3, pp. 295-360
[8] Some penalisations of the Wiener measure, Japan. J. Math., Volume 1 (2006), pp. 263-290
[9] B. Roynette, M. Yor, Penalising Brownian paths: Rigorous results and meta-theorems, Laboratoire de Probabilités et Modèles Aléatoires, Prépublication, 2007
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