Institute of Mathematical Statistics Lecture Notes - Monograph Series

Strong invariance principle for dependent random fields

Alexander Bulinski and Alexey Shashkin

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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.

Chapter information

Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy, eds., Dynamics & Stochastics: Festschrift in honor of M. S. Keane (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 128-143

First available in Project Euclid: 28 November 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F15: Strong theorems 60F17: Functional limit theorems; invariance principles

dependent random fields weak dependence association covariance inequalities strong invariance principle law of the iterated logarithm

Copyright © 2006, Institute of Mathematical Statistics


Bulinski, Alexander; Shashkin, Alexey. Strong invariance principle for dependent random fields. Dynamics & Stochastics, 128--143, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000167.

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