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 Electronic Journal of Probability > Vol. 10 (2005) > Paper 38 open journal systems 


Limit Theorems for Self-normalized Large Deviation

Qiying WANG, School of Maths and Stats, University of Sydney


Abstract
Let $X, X_1, X_2, cdots $ be i.i.d. random variables with zero mean and finite variance $si^2$. It is well known that a finite exponential moment assumption is necessary to study limit theorems for large deviation for the standardized partial sums. In this paper, limit theorems for large deviation for self-normalized sums are derived only under finite moment conditions. In particular, we show that, if $EX^4
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Pages: 1260-1285

Published on: November 14, 2005
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Electronic Journal of Probability. ISSN: 1083-6489