一类随机变量序列加权和的Chover型重对数律

Law of Iterated Logarithm for the Weighted Partial Sums

对于具有某种尾渐近行为的独立同分布的随机变量序列,本文通过积分检验刻划了其加权部分和的极限结果,并作为推论获得了Chover型重对数律。把这些结果应用到经典的可和方式,获得了相应的结果。

We establish the integral test for the weighted partial sums of independent identically distributed random variables with a certain tail behavior assumption, and obtain the Chover's law of iterated logarithm (LIL) as a corollary. As applications, the corresponding limit results for some classical summability methods are also established.