A Self-normalized Law of the Iterated Logarithm for the Geometrically Weighted Random Series

Ke Ang FU^{1}, Wei HUANG^{2}

1 School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, P. R. China;
2 Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China

Let {X,X_{n}; n ≥ 0} be a sequence of independent and identically distributed random variables with EX = 0, and assume that EX^{2}I(|X| ≤ x) is slowly varying as x→∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series ∑_{n=0}^{∞}β^{n}X_{n} (0 < β < 1) is obtained, under some minimal conditions.

Supported by National Natural Science Foundation of China (Grant Nos. 11301481, 11371321 and 10901138), National Statistical Science Research Project of China (Grant No. 2012LY174), Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ12A01018), the Fundamental Research Funds for the Central Universities and Zhejiang Provincial Key Research Base for Humanities and Social Science Research (Statistics)

Ke Ang FU,Wei HUANG. A Self-normalized Law of the Iterated Logarithm for the Geometrically Weighted Random Series[J]. Acta Mathematica Sinica, English Series, 2016, 32(3): 384-392.

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