Full Text:
<2112>
CLC number: O211.4
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 0000-00-00
Cited: 0
Clicked: 4023
A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS
| |||||||||||||
ZHANG Li-xin, WEN Ji-wei. A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS[J]. Journal of Zhejiang University Science A, 2001, 2(1): 79-83.
@article{title="A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS",
author="ZHANG Li-xin, WEN Ji-wei",
journal="Journal of Zhejiang University Science A",
volume="2",
number="1",
pages="79-83",
year="2001",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.2001.0079"
}
%0 Journal Article
%T A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS
%A ZHANG Li-xin
%A WEN Ji-wei
%J Journal of Zhejiang University SCIENCE A
%V 2
%N 1
%P 79-83
%@ 1869-1951
%D 2001
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2001.0079
TY - JOUR
T1 - A LIMIT RESULT FOR SELF-NORMALIZED RANDOM SUMS
A1 - ZHANG Li-xin
A1 - WEN Ji-wei
J0 - Journal of Zhejiang University Science A
VL - 2
IS - 1
SP - 79
EP - 83
%@ 1869-1951
Y1 - 2001
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2001.0079
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.
[1] Chernoff,H.,1952.A measure of asymptotic efficiency for tests of a hypothesis based on sums of observations,Ann.Math.Statist.,23: 493-507.
[2] Csörgö,M.and Shao,Q.M.,1994.A self-normalized Erdös-Rényi type strong law of large numbers.Stoch.Processes Appl.,50: 187-196.
[3] Erdös,P.and Rényi,A.,1970.On a new law of large numbers. J. Analyze Math., 23: 103-111.
[4] Griffin,P.S.and Kuelbs,J.D.,1989.Self-normalized laws of the iterated logarithm. Ann. Probab., 17: 1571-1601.
[5] Révész,P.,1990.Random Walk in Random and Non-random Environments,World Scientific,Singapore.
[6] Shao,Q.M.,1995.On a conjecture of Révész, Proc. Amer. Soc., 123: 575-582.
[7] Shao,Q.M.,1997.Self-normalized Large Deviations. Ann. Probab., 25: 285-328.
[8] Zhang,L.X.,1998.Sufficient and necessary conditions for limit laws on lag sums of i.i.d.r.v.s.Acta Math.Sinica.New Series. 14: 113-124.
Open peer comments: Debate/Discuss/Question/Opinion
<1>