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.

引用

页码：103 / 120

页数：18

共 50 条

[41] Limit theorems for conditional distributions with regard for large deviations
Zaigraev A.Yu.
Ukrainian Mathematical Journal, 1999, 51 (8) : 1188 - 1200
[42] Some Strong Limit Theorems Represented by Inequalities
Jin, Shaohua
Sun, Shuguang
Wan, Yanping
Chen, Xiuyin
PROCEEDINGS OF FIRST INTERNATIONAL CONFERENCE OF MODELLING AND SIMULATION, VOL II: MATHEMATICAL MODELLING, 2008, : 44 - 49
[43] On the Lin Condition in Strong Ratio Limit Theorems
M. G. Shur
Mathematical Notes, 2004, 75 : 864 - 876
[44] Strong Limit Theorems for Increments of Random Fields
Taylor, Jonathan
STOCHASTIC GEOMETRY, SPATIAL STATISTICS AND RANDOM FIELDS: ASYMPTOTIC METHODS, 2013, 2068 : 385 - 398
[45] STRONG RATION LIMIT THEOREMS FOR MARKOV PROCESSES
LIN, M
ANNALS OF MATHEMATICAL STATISTICS, 1972, 43 (02): : 569 - &
[46] Majorizing potentials in strong ratio limit theorems
Shur, M. G.
MATHEMATICAL NOTES, 2008, 84 (1-2) : 116 - 124
[47] On the Lin condition in strong ratio limit theorems
Shur, MG
MATHEMATICAL NOTES, 2004, 75 (5-6) : 864 - 876
[48] Strong limit theorems for arbitrary stochastic sequences
Yang, Weiguo
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 326 (02) : 1445 - 1451
[49] Strong limit theorems for increments of renewal processes
Frolov A.N.
Journal of Mathematical Sciences, 2005, 128 (1) : 2614 - 2624
[50] Majorizing potentials in strong ratio limit theorems
M. G. Shur
Mathematical Notes, 2008, 84 : 116 - 124

← 1 2 3 4 5 →