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ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2001, Vol. 2 Issue (1): 79-83    DOI: 10.1631/jzus.2001.0079
Science & Engineering     
A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS
ZHANG Li-xin, WEN Ji-wei
Department of Mathematics,Zhejiang University,Hangzhou 310028,China
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Abstract  Suppose {X,Xn;n≥1} is a sequence i.i.d.r.v. with EX=0 and EX2<∞. Shao (1995) proved a conjecture of Révész (1990): if P(X=±1)=1/2, then ... Furthermore he conjectured that ... In this paper we prove that if supb>0P(X=b)≥P(X=0) then this conjecture is true.

Key words： self-normalized,i.i.d.random variables,Chernoff function     
Received: 18 October 1999     
CLC:  O211.4  
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WEN Ji-wei
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Cite this article:

ZHANG Li-xin, WEN Ji-wei. A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2001, 2(1): 79-83.

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http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.2001.0079     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2001/V2/I1/79

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