The Annals of Probability

A strong invariance principle for associated random fields

Raluca M. Balan

Full-text: Open access

Abstract

In this paper we generalize Yu’s [Ann. Probab. 24 (1996) 2079–2097] strong invariance principle for associated sequences to the multi-parameter case, under the assumption that the covariance coefficient u(n) decays exponentially as n→∞. The main tools that we use are the following: the Berkes and Morrow [Z. Wahrsch. Verw. Gebiete 57 (1981) 15–37] multi-parameter blocking technique, the Csörgő and Révész [Z. Wahrsch. Verw. Gebiete 31 (1975) 255–260] quantile transform method and the Bulinski [Theory Probab. Appl. 40 (1995) 136–144] rate of convergence in the CLT.

Article information

Source
Ann. Probab., Volume 33, Number 2 (2005), 823-840.

Dates
First available in Project Euclid: 3 March 2005

Permanent link to this document
https://projecteuclid.org/euclid.aop/1109868602

Digital Object Identifier
doi:10.1214/009117904000001071

Mathematical Reviews number (MathSciNet)
MR2123212

Zentralblatt MATH identifier
1070.60032

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 60G60: Random fields
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Strong invariance principle associated random fields blocking technique quantile transform

Citation

Balan, Raluca M. A strong invariance principle for associated random fields. Ann. Probab. 33 (2005), no. 2, 823--840. doi:10.1214/009117904000001071. https://projecteuclid.org/euclid.aop/1109868602


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References

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