Abstract
Let X, X1, X2,... be a sequence of independent and identically distributed random variables in the domain of attraction of a normal distribution. A universal result in almost sure limit theorem for the self-normalized partial sums S n /V n is established, where . Mathematical Scientific Classification: 60F15.
Highlights
Throughout this article, we assume {X, Xn}n Î N is a sequence of independent and identically distributed (i.i.d.) random variables with a non-degenerate distribution function F
We say that the random variable belongs to the domain of attraction of the normal law, if there exist constants an > 0, bn Î R such that
Let {X, Xn}nÎN be a sequence of i.i.d. random variables in the domain of attraction of the normal law with mean zero
Summary
A note on the almost sure limit theorem for selfnormalized partial sums of random variables in the domain of attraction of the normal law Qunying Wu1,2. Edu.cn 1College of Science, Guilin University of Technology, Guilin 541004, P. R. China Full list of author information is available at the end of the article
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