独立随机变量序列的强大数定律

The Strong Law of Large Numbers of Independent Random Variables Sequence

将刘文的分析方法应用于独立随机变量序列,得到了序列服从强大数定律的一个与指数矩相关的充分条件如下:存在一个正数δ使得对所有正整数n,δX_n 与-δX_n的指数矩都有限,且对趋于无穷的正数序列{b_n},λΧ_j的指数矩的λ分之一次幂的自然对数与-λΧ_j的指数矩的一λ分之一次幂的自然对数的差,被b_n除,对j从1到n求和,和式当n趋于无穷时的上极限当正数入趋于零时收敛于零。

Applying Liu Wen analytic approach to the independent random variables sequence, One of the sufficient conditions correlating to the expo-nential moments is obtained in which the sequence is made obedient to the strong law of large numbers is shown as follows: Having existed a positive number, it will make all the positive integers n and the expon-ential moments of both δX_n and-δX_n finite, and for a positive number sequence{b_n}which tends to infinity, the sum of difference between the natural logarithm of one λth power of the exponential moment of λx_j and the natural logarithm of one- λth power of the exponential moment of- λX_j, to be divided by b_n, (j counts from l to n) , it converges to zero as positive number λ tends to zero.