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http://dx.doi.org/10.4134/JKMS.2012.49.4.795

GENERAL LAWS OF PRECISE ASYMPTOTICS FOR SUMS OF RANDOM VARIABLES  

Meng, Yan-Jiao (Department of Mathematics China Jiliang University)
Publication Information
Journal of the Korean Mathematical Society / v.49, no.4, 2012 , pp. 795-804 More about this Journal
Abstract
In this paper, we obtain two general laws of precise asymptotics for sums of i.i.d random variables, which contain general weighted functions and boundary functions and also clearly show the relationship between the weighted functions and the boundary functions. As corollaries, we obtain Theorem 2 of Gut and Spataru [A. Gut and A. Sp$\check{a}$taru, Precise asymptotics in the law of the iterated logarithm, Ann. Probab. 28 (2000), no. 4, 1870-1883] and Theorem 3 of Gut and Sp$\check{a}$taru [A. Gut and A. Sp$\check{a}$taru, Precise asymptotics in the Baum-Katz and Davids laws of large numbers, J. Math. Anal. Appl. 248 (2000), 233-246].
Keywords
precise asymptotics; general law; weighted function; boundary function;
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