Let $F$ be a distribution function on $\lbrack 0, 1\rbrack^d$, and let $W_F$ be the Gaussian process that is the weak limit of the empirical process determined by $F$. If $G$ is a function on $\lbrack 0, 1\rbrack^d$, upper and lower bounds are found for $P(\sup_{t \in \lbrack 0, 1\rbrack^d}|W_F(t) - G(t)| \leq \varepsilon)$.
Publié le : 1988-01-14
Classification:
Brownian sheet,
Kolmogorov-Smirnov,
large deviations,
Haar functions,
empirical processes,
60G15,
60F10,
60G60,
62G10
@article{1176991899,
author = {Bass, Richard F.},
title = {Probability Estimates for Multiparameter Brownian Processes},
journal = {Ann. Probab.},
volume = {16},
number = {4},
year = {1988},
pages = { 251-264},
language = {en},
url = {http://dml.mathdoc.fr/item/1176991899}
}
Bass, Richard F. Probability Estimates for Multiparameter Brownian Processes. Ann. Probab., Tome 16 (1988) no. 4, pp. 251-264. http://gdmltest.u-ga.fr/item/1176991899/