A strong invariance principle for associated random fields

Details A strong invariance principle for associated random fields A strong invariance principle for associated random fields

2005-03-29

arxiv.org/abs/math/0503661v1

Annals of Probability 2005, Vol. 33, No. 2, 823-840

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000001071 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000001071

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\to \infty. 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 Csorgo and Revesz [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.

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