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http://dx.doi.org/10.4134/JKMS.2008.45.4.993

PRECISE RATES IN THE LAW OF THE LOGARITHM FOR THE MOMENT CONVERGENCE OF I.I.D. RANDOM VARIABLES

Pang, Tian-Xiao (Department of Mathematics Zhejiang University)
Lin, Zheng-Yan (Department of Mathematics Zhejiang University)
Jiang, Ye (College of Business and Administration Zhejiang University of Technology)
Hwang, Kyo-Shin (Research Institute of Natural Science Geongsang National University)

Publication Information

Journal of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 993-1005 More about this Journal

Abstract

Let { $X,\;X_n;n{\geq}1$ } be a sequence of i.i.d. random variables. Set $S_n=X_1+X_2+{\cdots}+X_n,\;M_n=\max_{k{\leq}n}|S_k|,\;n{\geq}1$ . Then we obtain that for any -1 if and only if EX=0 and $$EX^2={\sigma}^2$ < ${\infty}$$ .

Keywords

law of the logarithm; moment convergence; rate of convergence; strong approximation; i.i.d. random variables;

Citations & Related Records

Times Cited By Web Of Science : 1 (Related Records In Web of Science)
Times Cited By SCOPUS : 0

Reference

1	M. Csorgo and P. Revesz, Strong Approximations in Probability and Statistics, Probability and Mathematical Statistics. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981
2	P. Billingsley, Convergence of Probability Measures: Second edition, Wiley Series in Probability and Statistics: Probability and Statistics. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1999
3	U. Einmahl, The Darling-Erdos theorem for sums of i.i.d. random variables, Probab. Theory Related Fields 82 (1989), no. 2, 241-257 DOI
4	A. I. Sakhanenko, On estimates of the rate of convergence in the invariance principle, In Advances in Probability Theory: Limit Theorems and Related Problems (A. A. Borovkov, ed.) 124-135, Springer, New York, 1984
5	A. I. Sakhanenko, Convergence rate in the invariance principle for nonidentically distributed variables with exponential moment, In Advances in Probability Theory: Limit Theorems for Sums of Random Variables (A. A. Borovkov, ed.) 2-73. Springer, New York, 1985. Springer, New York
6	A. Gut and A. Spataru, Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000), no. 4, 1870-1883 DOI ScienceOn
7	W. Feller, The law of the iterated logarithm for identically distributed random variables, Ann. of Math. (2) 47 (1946), 631-638 DOI