A remark on LSL for weighted sums of i.i.d random elements

作者：Chen, Pingyan^*; Chen, Ran

来源：Statistics & Probability Letters, 2010, 80(17-18): 1329-1334.

DOI：10.1016/j.spl.2010.04.013

• Law of the single logarithm
• Random element
• Weighted sums

In the paper, the upper bound and lower bound of the law of the single logarithm (LSL) are established under the condition that the sequence of the normalized weighted sums of random elements is bounded in probability. The main result improves the upper bound in [Sung, S.H., 2009. A law of the single logarithm for weighted sums of i.i.d. random elements. Statist. Probab. Lett., 79,1351-1357] and hence extends the result in [Chen, P., Gan, S., 2007. Limiting behavior of weighted sums of i.i.d. random variables. Statist. Probab. Lett., 77,1589-1599].

• 出版日期2010-9-1
• 单位暨南大学