We show that the logarithm of the probability that the Brownian sheet has a supremum at most $\epsilon$ over $\lbrack 0, 1\rbrack^2$ is of order $\epsilon^{-2}(\log(1/\epsilon))^3$.
Publié le : 1994-07-14
Classification:
Probabilities for suprema,
probabilities for norms,
60E15,
60G17,
60B11,
28C20,
46A35,
46B20
@article{1176988605,
author = {Talagrand, Michel},
title = {The Small Ball Problem for the Brownian Sheet},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 1331-1354},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988605}
}
Talagrand, Michel. The Small Ball Problem for the Brownian Sheet. Ann. Probab., Tome 22 (1994) no. 4, pp. 1331-1354. http://gdmltest.u-ga.fr/item/1176988605/