A strong approximation of self-normalized sums

Let {X, Xn,n ≥ 1} be a sequence of independent identically distributed random variables with EX = 0 and assume that EX2I（｜X｜ ≤ x） is slowly varying as x → ∞, i.e., X is in the domain of attraction of the normal law. In this paper a Strassen-type strong approximation is established for self-normalize...

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Veröffentlicht in:	Science China. Mathematics 2013-01, Vol.56 (1), p.149-160
Hauptverfasser:	Csörgő, Miklós, Hu, ZhiShui
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Approximation Astronomy Attraction China en型 Infinity Law Mathematical analysis Mathematics Mathematics and Statistics Random variables Series (mathematics) Sums 吸引力强逼近慢变标准化独立同分布随机变量
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Zusammenfassung:	Let {X, Xn,n ≥ 1} be a sequence of independent identically distributed random variables with EX = 0 and assume that EX2I（｜X｜ ≤ x） is slowly varying as x → ∞, i.e., X is in the domain of attraction of the normal law. In this paper a Strassen-type strong approximation is established for self-normalized sums of such random variables.
ISSN:	1674-7283 1006-9283 1869-1862
DOI:	10.1007/s11425-012-4434-7