An exponential inequality and strong limit theorems for conditional expectations

被引：0
作者：
A. Chuprunov
I. Fazekas
机构：
[1] Chebotarev Inst. of Math. and Mechanics Kazan State University,Department of Math. Stat. and Probability
[2] University of Debrecen,Faculty of Informatics
来源：
Periodica Mathematica Hungarica | 2010年 / 61卷
关键词：
conditional expectation; moment; Khintchine’s inequality; exponential inequality; generalized allocation scheme; law of the iterated logarithm; strong law of large numbers; 60F15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
An exponential inequality for the tail of the conditional expectation of sums of centered independent random variables is obtained. This inequality is applied to prove analogues of the Law of the Iterated Logarithm and the Strong Law of Large Numbers for conditional expectations. As corollaries we obtain certain strong theorems for the generalized allocation scheme and for the nonuniformly distributed allocation scheme.
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页码：103 / 120
页数：17
相关论文
共 11 条
[1]  
Chuprunov A.(2005)Inequalities and strong laws of large numbers for random allocations Acta Math. Hungar. 109 163-182
[2]  
Fazekas I.(2009)Strong laws of large numbers for random forests Acta Math. Hungar. 124 59-71
[3]  
Chuprunov A.(2009)An inequality for moments and its applications to the generalized allocation scheme Publ. Math. Debrecen 76 271-286
[4]  
Fazekas I.(1982)The best constants in the Khintchine inequality Studia Math. 70 231-283
[5]  
Chuprunov A.(2003)Limit theorems for a generalized allocation scheme Diskret. Mat. 15 148-157
[6]  
Fazekas I.(1923)Über dyadische Brüche Math. Zeitschr. 18 109-116
[7]  
Haagerup U.(1962)Three new proofs and generalization of a theorem of IrvingWeiss Magyar Tud. Akad. Mat. Kutató Int. Közl. 7 203-214
[8]  
Kolchin A. V.(1958)Limiting distributions in some occupancy problems Ann. Math. Statist. 29 878-884
[9]  
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