We calculate crossing probabilities and one-sided last exit time densities for a class of moving barriers on an interval [0, T] via Schwartz distributions. We derive crossing probabilities and first hitting time densities for another class of barriers on [0, T] by proving a Schwartz distribution version of the method of images. Analytic expressions for crossing probabilities and related densities are given for new explicit and semi-explicit barriers.
Publié le : 2008-08-15
Classification:
Brownian motion,
boundary-crossing probability,
moving barrier,
first hitting time density,
last exit time density,
Schwartz distribution,
reflection principle,
60J65,
60G40,
60J60
@article{1216677127,
author = {Kahale, Nabil},
title = {Analytic crossing probabilities for certain barriers by Brownian motion},
journal = {Ann. Appl. Probab.},
volume = {18},
number = {1},
year = {2008},
pages = { 1424-1440},
language = {en},
url = {http://dml.mathdoc.fr/item/1216677127}
}
Kahale, Nabil. Analytic crossing probabilities for certain barriers by Brownian motion. Ann. Appl. Probab., Tome 18 (2008) no. 1, pp. 1424-1440. http://gdmltest.u-ga.fr/item/1216677127/