| 傅可昂;张立新.B值强混合随机变量几何加权级数的广义重对数律[J].数学年刊A辑,2012,33(1):17~ |
| B值强混合随机变量几何加权级数的广义重对数律 |
| A Generalized Law of the Iterated Logarithm for Geometrically Weighted Series of B-valued Strong Mixing Random Variables |
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| DOI： |
| 中文关键词: Banach 空间, 混合相依,几何加权级数, 重对数律 |
| 英文关键词:Banach space, Mixing dependence, Geometrically weighted series, Law of the iterated logarithm |
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| 中文摘要: |
| 设 $\{X,X_{n};n\ge0\}$ 是一取值于可分 Banach 空间中的同分布 $\phi^\ast$-混合随机变量序列,并记其几何加权级数为 $\xi(\beta)=\sum\limits_{n=0}^\infty\beta^nX_n$, 其中 $0<\beta<1$. 在 $X$ 的二阶矩可能不存在的条件下,建立了 $\xi(\beta)$ 的一个广义重对数律. |
| 英文摘要: |
| Let {X,Xn; n > 0} be a sequence of identically distributed φ?-mixing dependentrandom variables taking values in a separable Banach space, and define its geometricallyweighted series ξ(β) =∞ Pn=0βnXn for 0 < β < 1. In this paper, a general law of the iteratedlogarithm for ξ(β) is established under the assumption that the second moment of X mightbe infinite. |
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