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October 1996 A strong invariance principle for associated sequences
Hao Yu
Ann. Probab. 24(4): 2079-2097 (October 1996). DOI: 10.1214/aop/1041903219


By combining the Berkes-Philipp blocking technique and the Csörgö-Révész quantile transform methods, we find that partial sums of an associated sequence can be approximated almost surely by partial sums of another sequence with Gaussian marginals. A crucial fact is that this latter sequence is still associated with covariances roughly bounded by the covariances of the original sequence, and that one can approximate it by an iid Gaussian process using the Berkes-Philipp method. We require that the original sequence has finite $(2 + r)$th moments, $r > 0$, and a power decay rate of a coefficient $u(n)$ which describes the covariance structure of the sequence. Based on this result, we obtain a strong invariance principle for associated sequences if $u(n)$ exponentially decreases to 0.


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Hao Yu. "A strong invariance principle for associated sequences." Ann. Probab. 24 (4) 2079 - 2097, October 1996.


Published: October 1996
First available in Project Euclid: 6 January 2003

zbMATH: 0879.60028
MathSciNet: MR1415242
Digital Object Identifier: 10.1214/aop/1041903219

Primary: 60B10 , 60F15 , 60F17
Secondary: 62G30

Keywords: association , blocking technique , partial sums , quantile transform , Strong invariance principle

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.24 • No. 4 • October 1996
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