NSD序列的Chover型重对数律

Chover's Law of Iterated Logarithm for NSD Sequence

设{X,X_n,n≥1}是同分布的负超可加相依(NSD)序列,满足X为α重尾的.利用NSD序列的矩不等式及正则变化函数的性质证明依概率1有lim sup n→∞(n∑i=1 X_i/B(n)1/loglogn=e^(1/a),其中B(x)是指数为1/α的正则变化函数,并获得了一系列等价条件.

Let{X,X n,n≥1}be an identically distributed negatively superadditive dependent(NSD)sequence with X satisfying heavy-tailed distribution with characteristic exponentα.By using the moment inequalities for NSD sequence and the properties of the regularly varying functions,we proved that,with probability 1,lim sup n→∞∑n i=1 X i B(n)1[]loglog n=e 1/α,where B(x)is a regularly varying fu nction with characteristic exponent 1/α.And a series of equivalent condition s were obtained.