自正则化和重对数律的极限定理

Limit theorem for LIL of self-normalized sums

设X,X1,X2,Λ是独立同分布的随机变量序列,记■。

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.