General maximal inequalities related to the strong law of large numbers

被引：2

作者：

Levental, S. ^{[1
]}

Salehi, H. ^{[1
]}

Chobanyan, S. A. ^{[1
]}

机构：

[1] Michigan State Univ, E Lansing, MI 48824 USA

来源：

MATHEMATICAL NOTES | 2007年 / 81卷 / 1-2期

关键词：

strong law of large numbers; quasistationary random sequence; Banach space; Hilbert space; Bochner measurability; Jensen's inequality;

D O I：

10.1134/S0001434607010087

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For any sequence (xi(n)) of random variables, we obtain maximal inequalities from which we can derive conditions for the a.s. convergence to zero of the normalized differences [GRAPHICS] The convergence to zero of this sequence leads to the Strong law Of large numbers (SLLN). In the special case of quasistationary sequences, we obtain a sufficient condition for the SLLN this condition is an improvement on the well-known Moriez conditions.

引用

页码：85 / 96

页数：12

共 14 条

[1] Strong law of large numbers under a general moment condition [J].