应用概率统计
應用概率統計
응용개솔통계
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS
2006年
2期
201-207
,共7页
强大数定律%弱相依随机变量%混合随机变量%p可光滑的Banach空间
彊大數定律%弱相依隨機變量%混閤隨機變量%p可光滑的Banach空間
강대수정률%약상의수궤변량%혼합수궤변량%p가광활적Banach공간
Strong law of large number%weakly dependent random variable%mixing random variable%p-smoothable Banach space
本文在Banaclh空间B是p可光滑(1＜p≤2)的条件下获得了B值弱相依随机变量序列正则和极限点集的上界.作为应用,由B值y-混合随机变量序列的强大数定律刻划了Banach空间的p可光滑性,在不要求混合系数(φ)n和ψn趋于0而是在inf n≥1(φ)n=0或inf n≥1ψn=0的条件下,获得了B值相依随机变量序列有关强大数定律的一些结果.
本文在Banaclh空間B是p可光滑(1＜p≤2)的條件下穫得瞭B值弱相依隨機變量序列正則和極限點集的上界.作為應用,由B值y-混閤隨機變量序列的彊大數定律刻劃瞭Banach空間的p可光滑性,在不要求混閤繫數(φ)n和ψn趨于0而是在inf n≥1(φ)n=0或inf n≥1ψn=0的條件下,穫得瞭B值相依隨機變量序列有關彊大數定律的一些結果.
본문재Banaclh공간B시p가광활(1＜p≤2)적조건하획득료B치약상의수궤변량서렬정칙화겁한점집적상계.작위응용,유B치y-혼합수궤변량서렬적강대수정률각화료Banach공간적p가광활성,재불요구혼합계수(φ)n화ψn추우0이시재inf n≥1(φ)n=0혹inf n≥1ψn=0적조건하,획득료B치상의수궤변량서렬유관강대수정률적일사결과.
In this paper, we obtain the almost sure bound of normal sum of B-valued weakly dependent random variables under the assumption that Banach space B is p-smoothable (1 ＜ p ≤ 2). As its application, we characterize p-smoothness of Banach space through the strong law of large mumbers of B-valued y-mixing random variables, and obtain some results on the strong law of large numbers for B-valued dependent random variables without assumption on rate of tending to zero of (φ) and ψ-mixing parameters (φ)n and ψn but under the assumption that infn≥1(φ)n = 0 or infn≥1 ψn = 0 respectively.
