NA列自正则某些部分和乘积的几乎处处中心极限定理

Almost sure central limit theorem for self-normalized products of some partial sums of NA random variables

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k(k∏(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=∑Xj-Xi,1≤i=1j=1k i≤k,V2k=∑(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。

Let { X,Xn}n∈Nbe a stationary sequence of NA positive random variables. W e proved an alm ost sure k central lim it theorem for the self-norm alized products of som e partial sum s（ ∏（ Sk,i/（（ k- 1） μ）））μ /（ βVk）,where i = 1k kβ 0 was a constant,E（ X） = μ,S2 k,i= ∑Xj- Xi,1 ≤ i ≤ k,V k= ∑（ Xi- μ）2. The results generalize not only j = 1i = 1on the weigh of the alm ost sure central lim it theorem but also in the range of random variables.