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- W2000833504 abstract "For a sequence of i.i.d. mean 0 random variables {X,Xn;n≥1} with weighted partial sums Sn(X,w(⋅))=∑k=1nw(kn)Xk,n≥1 where w(t),0≤t≤1 is a Lipschitz function of order 1 with ‖w(⋅)‖2=∫01w2(t)dt>0, necessary and sufficient conditions are provided for X to enjoy iterated logarithm type behavior of the form 0<lim supn→∞|Sn(X,w(⋅))|/nh(n)<∞ almost surely where h(⋅) is a positive, nondecreasing function which is slowly varying at infinity. Some corollaries are presented for particular choices of h(⋅)." @default.
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- W2000833504 date "2009-03-01" @default.
- W2000833504 modified "2023-09-23" @default.
- W2000833504 title "Iterated logarithm type behavior for weighted sums of i.i.d. random variables" @default.
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- W2000833504 doi "https://doi.org/10.1016/j.spl.2008.10.010" @default.
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