A Baum-Katz theorem for i.i.d. random variables with higher order moments

作者：Chen, Pingyan; Sung, Soo Hak^*

来源：Statistics & Probability Letters, 2014, 94: 63-68.

DOI：10.1016/j.spl.2014.07.005

• Baum-Katz law
• Sums of i.i.d. random variables
• Convergence rates

For a sequence of i.i.d. random variables {X, X-n, n >= 1} with EX = 0 and E exp{(log vertical bar X vertical bar(alpha)} < infinity for some alpha > 1, Gut and Stadtmilller (2011) proved a Baum-Katz theorem. In this paper, it is proved that E exp{(log vertical bar X vertical bar(alpha)} < infinity if and only if Sigma(infinity)(n=1) exp{(logn}(alpha)}n(-2)(log n)(alpha-1) P(vertical bar S-n vertical bar > n) < infinity, where S-n = Sigma(n)(i=1) X-i. This result improves the corresponding one of Gut and Stadtmuller (2011).

• 出版日期2014-11
• 单位暨南大学