摘要
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.
出处
《河北工业大学学报》
CAS
1993年第3期82-89,共8页
Journal of Hebei University of Technology
关键词
强大数定律
独立随机变数序列
指数矩
条件期望
分析方法
充分条件
δ区间
单调函数
The strong law of large numbers
Independent random variables sequence
The exponential moment
Conditional expectation
Analytic approach
Sufficient condition
δ interval
Monotone function
