摘要
本文讨论了滑动和过程的Spitzer和Baum-Katz律的精确渐近,其中{ξ,ξi-∞<i<∞}是双向无穷的独立同分布的随机变量序列,其共同分布属于某个半稳定律的(正则)吸引场,{ci,-∞<i<∞}满足某种可和条件的实数序列.为此,建立了Xk的一个基本定理,其本身也是有意义的.
In this paper, we discuss the precise asymptotics in Spitzer and Baum-Katz＇s law of large numbers for the moving average processes Xk=∑i=-∞^＋∞ ciξk-i where {ξ,ξi-∞ 〈i〈∞）is a doubly infinite sequence of i.i.d, random variables with the distribution of ξ inthe （normal） domain of semistable attraction of.a semistable law, and {ci,-∞〈i〈∞）a sequence Of real numbers satisfying some summable condition. For this purpose, we also establish the general central limit theorem for Xk, which is of independent interest.
出处
《应用数学学报》
CSCD
北大核心
2007年第6期1011-1017,共7页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(No.60574002)资助项目.
