A universal result in almost sure central limit theory
نویسندگان
چکیده
منابع مشابه
A Note for Extension of Almost Sure Central Limit Theory
for any continuity point x of H . Several papers have dealt with logarithmic limit theorems of this kind and the above relation has been extended in various directions. Fahrner and Stadtmüller [5] gave an almost sure version of a maximum limit theorem. Berkes and Horváth [2] obtained a strong approximation for the logarithmic average of sample extremes. Berkes and Csáki [1] showed that not only...
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Let {Xn; n ≥ 1} be a standardized non-stationary Gaussian sequence, and let denote Sn ∑n k 1 Xk , σn √ Var Sn . Under some additional condition, let the constants {uni; 1 ≤ i ≤ n, n ≥ 1} satisfy ∑n i 1 1−Φ uni → τ as n → ∞ for some τ ≥ 0 and min1≤i≤n uni ≥ c logn , for some c > 0, then, we have limn→∞ 1/ logn ∑n k 1 1/k I{∩i 1 Xi ≤ uki , Sk/σk ≤ x} e−τΦ x almost surely for any x ∈ R, where I A ...
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Copyright q 2012 Yu Miao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We obtain the almost sure central limit theorem ASCLT of sample quantiles. Furthermore, based on the method, the ASCLT of order statistics is also pro...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2001
ISSN: 0304-4149
DOI: 10.1016/s0304-4149(01)00078-3