Strong approximation for sums of asymptotically negatively dependent Gaussian sequences with applications

K.-A. Fu; L.-X. Zhang

doi:10.1007/s10474-009-8214-y

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Acta Mathematica Hungarica

Volume/Issue:: Volume 125: Issue 1-2

Strong approximation for sums of asymptotically negatively dependent Gaussian sequences with applications

Authors: K.-A. Fu¹ and L.-X. Zhang¹

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¹ Zhejiang Gongshang University School of Statistics and Mathematics Hangzhou 310018 China

DOI:: https://doi.org/10.1007/s10474-009-8214-y

Page Count:: 47–64

Publication Date:: 01 Oct 2009

Online Publication Date:: 11 Nov 2009

Article Category:: Research Article

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Abstract

By applying the Skorohod martingale embedding method, a strong approximation theorem for partial sums of asymptotically negatively dependent (AND) Gaussian sequences, under polynomial decay rates, is established. As applications, the law of the iterated logarithm, the Chung-type law of the iterated logarithm and the almost sure central limit theorem for AND Gaussian sequences are derived.