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滑动平均过程的Spitzer和Baum-Katz律的精确渐近
  • 期刊名称：应用数学学报， 2007，30(6), 06，
  • 时间：0
  • 分类：O211.4[理学—概率论与数理统计;理学—数学]
  • 作者机构：[1]暨南大学数学系,广州510630, [2]暨南大学统计学系,广州510630
  • 相关基金：国家自然科学基金（No.60574002）资助项目.
  • 相关项目：排队系统的最优控制及其应用的研究
关键词： 滑动平均过程, 半稳定分布, Spitzer律, Baum-Katz律, moving-average process, semistable distribution, Spitzer＇s law, Baum-Katz＇s law
中文摘要：

本文讨论了滑动和过程的Xk=∑i=-∞^＋∞ ciξk-i 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．

英文摘要：

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.

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排队系统的最优控制及其应用的研究
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