ON THE RATES OF THE ALMOST SURE CONVERGENCE FOR SELF-NORMALIZED LAW OF THE ITERATED LOGARITHM

- Journal title : Bulletin of the Korean Mathematical Society
- Volume 48, Issue 6, 2011, pp.1137-1146
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/BKMS.2011.48.6.1137

Title & Authors

ON THE RATES OF THE ALMOST SURE CONVERGENCE FOR SELF-NORMALIZED LAW OF THE ITERATED LOGARITHM

Pang, Tian-Xiao;

Pang, Tian-Xiao;

Abstract

Let {, } be a sequence of i.i.d. nondegenerate random variables which is in the domain of attraction of the normal law with mean zero and possibly infinite variance. Denote , and . Then for d > -1, we showed that under some regularity conditions, holds in this paper, where If g denotes the indicator function.

Keywords

almost sure convergence;self-normalized;domain of attraction of the normal law;law of the iterated logarithm;

Language

English

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