This paper presents correction terms to the tangent approximation for the first-exit density of Brownian motion at distant boundaries. These lead to second-order approximations to the first-exit distribution. Asymptotic formulas for the mean and variance of the first-exit time are derived. Numerical comparisons show the accuracy of the approximations.
Publié le : 1985-02-14
Classification:
First-exit time,
Brownian motion,
sequential tests,
62L10,
60G40,
60J65
@article{1176993071,
author = {Jennen, Christel},
title = {Second-Order Approximations to the Density, Mean and Variance of Brownian First-Exit Times},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 126-144},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993071}
}
Jennen, Christel. Second-Order Approximations to the Density, Mean and Variance of Brownian First-Exit Times. Ann. Probab., Tome 13 (1985) no. 4, pp. 126-144. http://gdmltest.u-ga.fr/item/1176993071/