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March 2005 A strong invariance principle for associated random fields
Raluca M. Balan
Ann. Probab. 33(2): 823-840 (March 2005). DOI: 10.1214/009117904000001071

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.

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Raluca M. Balan. "A strong invariance principle for associated random fields." Ann. Probab. 33 (2) 823 - 840, March 2005. https://doi.org/10.1214/009117904000001071

Information

Published: March 2005
First available in Project Euclid: 3 March 2005

zbMATH: 1070.60032
MathSciNet: MR2123212
Digital Object Identifier: 10.1214/009117904000001071

Subjects:
Primary: 60F17 , 60G60
Secondary: 60K35

Keywords: associated random fields , blocking technique , quantile transform , Strong invariance principle

Rights: Copyright © 2005 Institute of Mathematical Statistics

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