[Sur les premiers instants de croisement du mouvement brownien et d'une famille de courbes continues]
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.
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.
Accepté le :
Publié le :
Larbi Alili 1 ; Pierre Patie 2
@article{CRMATH_2005__340_3_225_0, author = {Larbi Alili and Pierre Patie}, 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}, }
Larbi Alili; Pierre Patie. On the first crossing times of a Brownian motion and a family of continuous curves. Comptes Rendus. Mathématique, Volume 340 (2005) no. 3, pp. 225-228. doi : 10.1016/j.crma.2004.11.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.11.008/
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