Strong invariance principle for dependent random fields

Details Strong invariance principle for dependent random fields Strong invariance principle for dependent random fields

2006-08-10

arxiv.org/abs/math/0608237v1

IMS Lecture Notes--Monograph Series 2006, Vol. 48, 128-143

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921706000000167 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000167

A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative association. We use the approach of Cs\"{o}rg\H{o} and R\'{e}v\'{e}sz applied recently by Balan to associated random fields. The key step in our proof combines new moment and maximal inequalities, established by the authors for partial sums of multiindexed random variables, with the estimate of the convergence rate in the CLT for random fields under consideration.

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