AN EXPONENTIAL INEQUALITY AND STRONG LIMIT THEOREMS FOR CONDITIONAL EXPECTATIONS

被引：4
|
作者：
Chuprunov, A. [1 ]
Fazekas, I. [2 ]
机构：
[1] Kazan VI Lenin State Univ, Dept Math Stat & Probabil, Chebotarev Inst Math & Mech, Kazan 420008, Russia
[2] Univ Debrecen, Fac Informat, H-4010 Debrecen, Hungary
来源：
PERIODICA MATHEMATICA HUNGARICA | 2010年 / 61卷 / 1-2期
关键词：
conditional expectation; moment; Khintchine's inequality; exponential inequality; generalized allocation scheme; law of the iterated logarithm; strong law of large numbers;
D O I：
10.1007/s10998-010-3103-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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：18
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