In this paper we present an analytical proof of the fact that the maximum of gaussian random walks exceeds an arbitrary level b with a probability that is an increasing function of the step variances. An analogous result for stochastic integrals is also obtained.
@article{urn:eudml:doc:38921,
title = {How the maximum of gaussian random walks and fields is influenced by changes of the variances.},
journal = {Stochastica},
volume = {9},
year = {1985},
pages = {75-84},
zbl = {0588.60064},
mrnumber = {MR0823230},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38921}
}
Orsingher, Enzo. How the maximum of gaussian random walks and fields is influenced by changes of the variances.. Stochastica, Tome 9 (1985) pp. 75-84. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38921/