| 自正则化和重对数律的极限定理 |
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| 引用本文： | 袁裕泽.自正则化和重对数律的极限定理[J].闽江学院学报,2013,34(2):39-41. |
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| 作者姓名： | 袁裕泽 |
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| 作者单位： | 闽江学院数学系,福建福州,350121 |
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| 摘 要： | 设X,X1,X2,Λ是独立同分布的随机变量序列,记■。
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| 关 键 词： | 极限定理 重对数律 自正则化和 |
Limit theorem for LIL of self-normalized sums |
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| YUAN Yu-ze.Limit theorem for LIL of self-normalized sums[J].Journal of Minjiang University,2013,34(2):39-41. |
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| Authors: | YUAN Yu-ze |
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| Institution: | YUAN Yu-ze ( Department of Mathematics, Minjiang University, Fuzhou, Fujian 350121, China) |
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| Abstract: | Limit theorem for LIL of self-normalized sums YUAN Yu-ze （ Department of Mathematics, Minjiang University, Fuzhou, Fujian 350121, China） Abstract： Let X,X1 ,X2.… be i. i. d random sequences, setsn=n∑k=1Xi＋V2n=n∑k=1x2k＋ 且EX=0,EX2I（｜X｜≤x）is slowly varying at ~ ,we prove that, forb〉-1,limε ε-0 2（b＋1）∞∑n=1（loglogn）b/nlognP（｜sn/Vm｜≥ε√2loglogn）=1/（b＋1）√π）=Г（b＋3/2）here Г（ ·） is Gamma function. |
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| Keywords: | limit theorem law of iterated logarithm self-normalized sums |
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