A sufficient condition is given for a sequence of partial-sum set-indexed processes with nonuniform $\phi$-mixing condition to converge to Brownian motion. The main result (Theorem 1.1) is an extension of the similar results of Goldie and Greenwood by weakening the $\phi$-mixing condition. An application (Corollary 4.2) to certain Gibbs fields is given.
Publié le : 1991-04-14
Classification:
Nonuniform $\phi$-mixing condition,
random fields on integer lattice,
partial-sum process,
Brownian motion,
metric entropy,
Gibbs fields,
60F17,
60B10,
60K35
@article{1176990445,
author = {Chen, Dongching},
title = {A Uniform Central Limit Theorem for Nonuniform $\phi$-Mixing Random Fields},
journal = {Ann. Probab.},
volume = {19},
number = {4},
year = {1991},
pages = { 636-649},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990445}
}
Chen, Dongching. A Uniform Central Limit Theorem for Nonuniform $\phi$-Mixing Random Fields. Ann. Probab., Tome 19 (1991) no. 4, pp. 636-649. http://gdmltest.u-ga.fr/item/1176990445/