A SUPPLEMENT TO PRECISE ASYMPTOTICS IN THE LAW OF THE ITERATED LOGARITHM FOR SELF-NORMALIZED SUMS

- Journal title : Journal of the Korean Mathematical Society
- Volume 45, Issue 6, 2008, pp.1601-1611
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2008.45.6.1601

Title & Authors

A SUPPLEMENT TO PRECISE ASYMPTOTICS IN THE LAW OF THE ITERATED LOGARITHM FOR SELF-NORMALIZED SUMS

Hwang, Kyo-Shin;

Hwang, Kyo-Shin;

Abstract

Let X, , , ... be i.i.d. random variables with zero means, variance one, and set , . Gut and [3] established the precise asymptotics in the law of the iterated logarithm and Li, Nguyen and Rosalsky [7] generalized their result under minimal conditions. If P() is replaced by E{}+ in their results, the new one is called the moment version of precise asymptotics in the law of the iterated logarithm. We establish such a result for self-normalized sums, when X belongs to the domain of attraction of the normal law.

Keywords

precise asymptotics;law of iterated logarithm;self-normalized sums;

Language

English

References

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