非平稳NA随机变量域的重对数律

Law of the iterated logarithm for nonstationary negatively associated random fields

利用Rosenthal型最大值不等式、Kolmogorov型指数不等式及Stein方法,邵启满、苏淳就强平稳的NA随机变量于1999年建立了重对数律.本文利用与之类似的截尾方法,在期望为0,且2+τ阶距有限的条件下,得到了非平稳的NA随机变量域的重对数律.

SHAO and SU proved that the law of the iterated logarithm holds for a stationary negatively associated sequence of random variables with finite variance. The proof was based on a Rosenthal type maximal inequality, a Kolmogorov type exponential inequality and Stein's method. By using truncation method, a law is established of the iterated logarithm for nonstationary negatively associated random fields with EX1=0 and E|X1|2+τ<∞(for some τ>0).