Based on the well-known Borell inequality and on a general theorem for large and small increments of Banach space valued stochastic processes of Csaki, Csorgo and Shao, we establish some almost sure path behaviour of increments in general, and moduli of continuity in particular, for $l^p$-valued, $1 \leq p < \infty$, Gaussian processes with stationary increments. Applications to $l^p$-valued fractional Wiener and Ornstein-Uhlenbeck processes are also discussed. Our results refine and extend those of Csaki, Csorgo and Shao.
Publié le : 1993-10-14
Classification:
Banach space valued processes,
$l^p$-valued Gaussian,
fractional Wiener and Ornstein-Uhlenbeck processes,
path properties,
large increments and moduli of continuity,
60G15,
60G10,
60G17,
60F15,
60G07,
60F10
@article{1176989007,
author = {Csorgo, Miklos and Shao, Qi-Man},
title = {Strong Limit Theorems for Large and Small Increments of $l^p$-Valued Gaussian Processes},
journal = {Ann. Probab.},
volume = {21},
number = {4},
year = {1993},
pages = { 1958-1990},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989007}
}
Csorgo, Miklos; Shao, Qi-Man. Strong Limit Theorems for Large and Small Increments of $l^p$-Valued Gaussian Processes. Ann. Probab., Tome 21 (1993) no. 4, pp. 1958-1990. http://gdmltest.u-ga.fr/item/1176989007/