We establish new Kahane-Khintchine inequalities in Orlicz spaces induced by exponential Young functions for stationary real random fields which are bounded or satisfy some finite exponential moment condition. Next, we give sufficient conditions for partial sum processes indexed by classes of sets satisfying some metric entropy condition to converge in distribution to a set-indexed Brownian motion. Moreover, the class of random fields that we study includes $\phi$-mixing and martingale difference random fields.
Publié le : 2002-07-05
Classification:
Metric entropy,
Kahane-Khintchine inequalities,
Functional central limit theorem,
Invariance principle,
Martingale difference random fields,
Mixing random fields,
Orlicz spaces,
Metric entropy.,
60 F 05, 60 F 17, 60 G 60,
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
@article{hal-00488685,
author = {El Machkouri, Mohamed},
title = {Kahane-Khintchine inequalities and functional central limit theorem for random fields},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00488685}
}
El Machkouri, Mohamed. Kahane-Khintchine inequalities and functional central limit theorem for random fields. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00488685/