Open Access
VOL. 48 | 2006 Strong invariance principle for dependent random fields
Alexander Bulinski, Alexey Shashkin

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy

IMS Lecture Notes Monogr. Ser., 2006: 128-143 (2006) DOI: 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 Csörgő and Révész 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.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1130.60041
MathSciNet: MR2306195

Digital Object Identifier: 10.1214/074921706000000167

Primary: 60F15 , 60F17

Keywords: association , covariance inequalities , dependent random fields , Law of the iterated logarithm , Strong invariance principle , Weak dependence

Rights: Copyright © 2006, Institute of Mathematical Statistics

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