A note on random variables with an infinite absolute first moment

作者：Hu Tien Chung; Rosalsky Andrew^*

来源：Statistics & Probability Letters, 2015, 97: 212-215.

DOI：10.1016/j.spl.2014.11.024

• Infinite absolute first moment
• Sums of independent and identically distributed random variables
• Kolmogorov strong law of large numbers
• Almost sure convergence

In this correspondence, we prove that if X is a random variable with P (X = 0) = 0 and E|X| = infinity, then there exists a continuous function G on (0, infinity) with 0 < G (x) up arrow infinity and x/G(x) up arrow infinity as 0 < x up arrow infinity such that E (|X|G (|X|)) = infinity. An application of this result pertaining to the Kolmogorov strong law of large numbers is established.

• 出版日期2015-2
• 单位清华大学