We consider random walks with Gaussian distribution of summands. New
representations for Wiener-Hopf factorization components are obtained. The
factorization method is used to study the distribution of the excess over
one-sided and two-sided boundaries. Asymptotic expansions for these
distributions and for the expectation of the first exit time are obtained under
the assumption that the boundaries tend to infinity.
Publié le : 1996-10-14
Classification:
Random walks,
Wiener-Hopf factorization,
first exit time,
overshoot,
sequential probability ratio test,
60J15,
60G40,
60G50
@article{1041903223,
author = {Lotov, V. I.},
title = {On some boundary crossing problems for Gaussian random
walks},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 2154-2171},
language = {en},
url = {http://dml.mathdoc.fr/item/1041903223}
}
Lotov, V. I. On some boundary crossing problems for Gaussian random
walks. Ann. Probab., Tome 24 (1996) no. 2, pp. 2154-2171. http://gdmltest.u-ga.fr/item/1041903223/