滑动平均过程的Spitzer和Baum-Katz律的精确渐近  

Precise Asymptotic in Spitzer and Baum-Katz's Law of Large Numbers for Moving-average Processes

作　　者：陈平炎[1] 张华[2] 

机构地区：[1]暨南大学数学系,广州510630 [2]暨南大学统计学系,广州510630

出　　处：《应用数学学报》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.

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.

关 键 词：滑动平均过程 半稳定分布 Spitzer律 Baum-Katz律 

分 类 号：O211.4[理学—概率论与数理统计]