A law of the single logarithm for weighted sums of i.i.d. random elements

Soo Hak Sung

Statistics & Probability Letters, 2009, vol. 79, issue 10, 1351-1357

Abstract: Let {X,Xn,n>=1} be a sequence of i.i.d. Banach space valued random elements with E(||X||[beta]/(log||X||)[beta]/2) =1} an array of constants satisfying , where [alpha]>0, [beta]>0, and 1/2=1/[alpha]+1/[beta]. In this paper, we obtain a law of the single logarithm for weighted sums . We also obtain a strong law of large numbers for weighted sums of i.i.d. Banach space valued random elements with a suitable moment condition. No assumptions are made concerning the geometry of the underlying Banach space.

Date: 2009
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