多维欧氏空间中的一般重对数律的精确速率

Precise Rates in the Generalized Law of the Iterated Logarithm in Multidimensional Euclidean Space

摘要: 设\X,X_n,n\ge1\是一列满足\ep X=(0,0,\cdots,0)_m\times1和\cov(X,X)=\Sigma独立同分布的随机向量.对任意d>0和a_n=o((\ln\ln n)^-d),我们得到\pr(|S_n|\ge(\varepsilon+a_n)\sigma\sqrtn(\ln\ln n)^d)的一类加权无穷级数的一般重对数律的精确速率.

Abstract: Let \X,X_n,n\ge1\ be a sequence of i.i.d. random vectors with \ep X=(0,0,\cdots,0)_m\times1 and \cov(X,X)=\Sigma, and set S_n=\tsm_i=1^nX_i, n\ge1. For every d>0 and a_n=o((\ln\ln n)^-d), we obtain the precise rates in the generalized law of the iterated logarithm for a kind of weighted infiniteseries of \pr(|S_n|\ge(\varepsilon+a_n)\sigma\sqrtn(\ln\ln n)^d).