GENERAL LAWS OF PRECISE ASYMPTOTICS FOR SUMS OF RANDOM VARIABLES

Title & Authors
GENERAL LAWS OF PRECISE ASYMPTOTICS FOR SUMS OF RANDOM VARIABLES
Meng, Yan-Jiao;

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$\small{\check{a}}$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$\small{\check{a}}$taru [A. Gut and A. Sp$\small{\check{a}}$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;
Language
English
Cited by
1.
Convergence and Precise Asymptotics for Series Involving Self-normalized Sums, Journal of Theoretical Probability, 2016, 29, 1, 267
2.
Asymptotic results for hybrids of empirical and partial sums processes, Statistical Papers, 2014, 55, 4, 1121
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