In this paper we generalize Yu’s [Ann. Probab. 24 (1996) 2079–2097] strong invariance principle for associated sequences to the multi-parameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n→∞. The main tools that we use are the following: the Berkes and Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15–37] multi-parameter blocking technique, the Csörgő and Révész [Z. Wahrsch. Verw. Gebiete 31 (1975) 255–260] quantile transform method and the Bulinski [Theory Probab. Appl. 40 (1995) 136–144] rate of convergence in the CLT.
Publié le : 2005-03-14
Classification:
Strong invariance principle,
associated random fields,
blocking technique,
quantile transform,
60F17,
60G60,
60K35
@article{1109868602,
author = {Balan, Raluca M.},
title = {A strong invariance principle for associated random fields},
journal = {Ann. Probab.},
volume = {33},
number = {1},
year = {2005},
pages = { 823-840},
language = {en},
url = {http://dml.mathdoc.fr/item/1109868602}
}
Balan, Raluca M. A strong invariance principle for associated random fields. Ann. Probab., Tome 33 (2005) no. 1, pp. 823-840. http://gdmltest.u-ga.fr/item/1109868602/