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- 2016
NA列自正则某些部分和乘积的几乎处处中心极限定理
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Abstract:
摘要： 设{X,Xn}n∈N是平稳正的负相关(negatively associated, NA)随机变量序列,证明自正则某些部分和乘积(∏ki=1(Sk,i/((k-1)μ)))μ/(βVk)的几乎处处中心极限定理,其中β>0为一常数,E(X)=μ, Sk,i=∑kj=1Xj-Xi, 1≤i≤k, V2k=∑ki=1(Xi-μ)2。获得的结果不仅将其权重进行了推广而且也扩大了随机变量的范围。
Abstract: Let {X,Xn}n∈N be a stationary sequence of NA positive random variables. We proved an almost sure central limit theorem for the self-normalized products of some partial sums(∏ki=1(Sk,i/((k-1)μ)))μ/(βVk), where β>0 was a constant, E(X)=μ, Sk,i=∑kj=1Xj-Xi, 1≤i≤k, V2k=∑ki=1(Xi-μ)2. The results generalize not only on the weigh of the almost sure central limit theorem but also in the range of random variables
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