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Strong invariance principle for dependent random fields. (English) Zbl 1130.60041
Denteneer, Dee (ed.) et al., Dynamics and stochastics. Festschrift in honor of M. S. Keane. Selected papers based on the presentations at the conference ‘Dynamical systems, probability theory, and statistical mechanics’, Eindhoven, The Netherlands, January 3–7, 2005, on the occasion of the 65th birthday of Mike S. Keane. Beachwood, OH: IMS, Institute of Mathematical Statistics (ISBN 0-940600-64-1/pbk). Institute of Mathematical Statistics Lecture Notes - Monograph Series 48, 128-143 (2006).
Strong invariance principles are limit theorems concerning strong approximations for partial sums processes of some random sequence or field by a (multiparameter) Wiener process. The authors established a strong invariance principle for random fields which satisfy dependence conditions more general than positive or negative association. The authors use the approach of Csörgő and Révész applied recently by Balan to associated random fields. The key step in the 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 central limit theorem for random fields under consideration.
For the entire collection see [Zbl 1113.60008].

MSC:
60F17 Functional limit theorems; invariance principles
60G60 Random fields
60F15 Strong limit theorems
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