[Sur les premiers instants de croisement du mouvement brownien et d'une famille de courbes continues]
Nous examinons les transformations analytiques qui permettent de passer du mouvement brownien aux ponts browniens standards. Nous les généralisons et étudions certaines de leurs propriétés. L'image d'une courbe réelle et continue, par ces transformations, est une famille de courbes à laquelle nous nous intéressons. Nous établissons une relation simple et explicite entre les distributions des temps d'atteinte de chacun des éléments de cette famille par un mouvement brownien.
We review the analytic transformations allowing to construct standard Brownian bridges from a Brownian motion. These are generalized and some of their properties are studied. The new family maps the space of continuous positive functions into a family of curves which is the topic of our study. We establish a simple and explicit formula relating the distributions of the first hitting times of each of these curves by a standard Brownian motion.
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@article{CRMATH_2005__340_3_225_0,
author = {Alili, Larbi and Patie, Pierre},
title = {On the first crossing times of a {Brownian} motion and a family of continuous curves},
journal = {Comptes Rendus. Math\'ematique},
pages = {225--228},
publisher = {Elsevier},
volume = {340},
number = {3},
year = {2005},
doi = {10.1016/j.crma.2004.11.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.11.008/}
}
TY - JOUR AU - Alili, Larbi AU - Patie, Pierre TI - On the first crossing times of a Brownian motion and a family of continuous curves JO - Comptes Rendus. Mathématique PY - 2005 SP - 225 EP - 228 VL - 340 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.11.008/ DO - 10.1016/j.crma.2004.11.008 LA - en ID - CRMATH_2005__340_3_225_0 ER -
%0 Journal Article %A Alili, Larbi %A Patie, Pierre %T On the first crossing times of a Brownian motion and a family of continuous curves %J Comptes Rendus. Mathématique %D 2005 %P 225-228 %V 340 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.11.008/ %R 10.1016/j.crma.2004.11.008 %G en %F CRMATH_2005__340_3_225_0
Alili, Larbi; Patie, Pierre. On the first crossing times of a Brownian motion and a family of continuous curves. Comptes Rendus. Mathématique, Tome 340 (2005) no. 3, pp. 225-228. doi : 10.1016/j.crma.2004.11.008. http://www.numdam.org/articles/10.1016/j.crma.2004.11.008/
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