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  • Author or Editor: Khurelbaatar Gonchigdanzan x
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Summary In this note we prove an almost sure limit theorem for the products of U-statistics.

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Abstract

Let {Xn: n ≧ 1} be a sequence of dependent random variables and let {wnk: 1 ≦ kn, n ≧ 1} be a triangular array of real numbers. We prove the almost sure version of the CLT proved by Peligrad and Utev [7] for weighted partial sums of mixing and associated sequences of random variables, i.e.

limn1lognk=1n1kI(i=1kwkiXix)=12πxe12t2dta.s..

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