Refinement of convergence rates for tail probabilities

被引：32

作者：

Li, DL ^{[1
]}

Spataru, A

机构：

[1] Lakehead Univ, Dept Math Sci, Thunder Bay, ON P7B 5E1, Canada

[2] Romanian Acad, Inst Math Stat & Appl Math, Bucharest 76100 5, Romania

来源：

JOURNAL OF THEORETICAL PROBABILITY | 2005年 / 18卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

complete convergence; Hoffmann-Jorgensen inequality; large deviation; moderate deviation; law of large numbers; law of the iterated logarithm;

D O I：

10.1007/s10959-005-7534-2

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Let X-1, X-2,... be, i.i.d. random variables, and put S-n = X-1 + ... + X-n. We find necessary and sufficient moment conditions for integral(infinity)(epsilon) f(x(q))dx < infinity, epsilon > delta, where delta >= 0 and q > 0, and f (x) = Sigma(n) a(n)P(vertical bar S-n vertical bar > xb(n)) with a(n) > 0 and b(n) is either n(1/p), 0 < p < 2, root n log n or root n log log n. The series f (x) we deal with are classical series studied by Hsu and Robbins, Erdos, Spitzer, Baum and Katz, Davis, Lai, Gut, etc.

引用

页码：933 / 947

页数：15

共 20 条

[1]

[Anonymous], 1978, PROBABILITY THEORY

[2]

[Anonymous], INT J MATH MATH SCI

[3] ON THE MAXIMUM SEQUENCE IN A CRITICAL BRANCHING-PROCESS [J].

ATHREYA, KB .

ANNALS OF PROBABILITY, 1988, 16 (02) :502-507

[4] CONVERGENCE RATES IN LAW OF LARGE NUMBERS [J].

BAUM, LE ;

KATZ, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 120 (01) :108-&

[5] CONVERGENCE RATES FOR LAW OF ITERATED LOGARITHM [J].

DAVIS, JA .

ANNALS OF MATHEMATICAL STATISTICS, 1968, 39 (05) :1479-&

[6] CONVERGENCE RATES FOR PROBABILITIES OF MODERATE DEVIATIONS [J].

DAVIS, JA .

ANNALS OF MATHEMATICAL STATISTICS, 1968, 39 (06) :2016-&

[7] ON A THEOREM OF HSU AND ROBBINS [J].

ERDOS, P .

ANNALS OF MATHEMATICAL STATISTICS, 1949, 20 (02) :286-291

[8] CORRECTION [J].

ERDOS, P .

ANNALS OF MATHEMATICAL STATISTICS, 1950, 21 (01) :138-138

[9] CONVERGENCE-RATES FOR PROBABILITIES OF MODERATE DEVIATIONS FOR SUMS OF RANDOM-VARIABLES WITH MULTIDIMENSIONAL INDEXES [J].

GUT, A .

ANNALS OF PROBABILITY, 1980, 8 (02) :298-313

[10] COMPLETE CONVERGENCE AND THE LAW OF LARGE NUMBERS [J].

HSU, PL ;

ROBBINS, H .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1947, 33 (02) :25-31

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