Institute of Mathematical Statistics Lecture Notes - Monograph Series

Strong invariance principle for dependent random fields

Alexander Bulinski and Alexey Shashkin

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Abstract

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

Source
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

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196285815

Digital Object Identifier
doi:10.1214/074921706000000167

Mathematical Reviews number (MathSciNet)
MR2306195

Zentralblatt MATH identifier
1130.60041

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

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

Rights
Copyright © 2006, Institute of Mathematical Statistics

Citation

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. https://projecteuclid.org/euclid.lnms/1196285815


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