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

设（x，Xn；n≥0）是一取值于可分Banazh空间中的同分布Ф＊-混合随机变量序列，并记其几何加权级数为ξ（β）=∑∞n=0βnXn,其中0〈p〈1．在X的二阶矩可能不存在的条件下，建立了ξ（β）的一个广义重对数律．

Let {X,X_n;n≥0} be a sequence of identically distributed φ~*-mixing dependent random variables taking values in a separable Banach space,and define its geometrically weighted seriesζ(β) =sum from n=0 to ∞ β~n X_n for 0<β<1.In this paper,a general law of the iterated logarithm forζ(β) is established under the assumption that the second moment of X might be infinite.