%0 Journal Article
%T On the Law of the Iterated Logarithm for Products of Sums<br>和的乘积的重对数律
%A Chen Pingyan
%A <br>陈平炎
%J 数学物理学报(A辑)
%D 2008
%I 
%X Let $\{X,X_n,n\geq1\}$ be a stationary stochastic sequence ofindependent, or $\varphi$-mixing, or $\rho$-mixing positive random variables, or $\{X,X_n,n\geq1\}$ be a positive random variable sequence such that $\{X_n-EX,n\geq1\}$ is a stationary ergodic martingale differences, and set $S_n=\sum\limits^n_{j=1}X_j$ for $n\geq1 $. This paper proves certain law of the iterated logarithm for properly normalized products of the partial sums, $\prod\limits^n_{j=1}S_j/n!\mu^n$ when $EX=\mu>0$ and $0<{\rm Var}(X)<\infty$.
%K Product of sum
%K Laws of the iterated logarithm
%K Mixing sequence<br>部分和的乘积
%K 重对数律
%K 混合序列.
%K 乘积的
%K 重对数律
%K Products
%K 正则化因子
%K 条件
%K 鞅差序列
%K 平稳遍历
%K 随机变量序列
%K 混合
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=BC7759FFA14EFE9CF8A52E3689682444&yid=67289AFF6305E306&vid=D3E34374A0D77D7F&iid=CA4FD0336C81A37A&sid=5C3443B19473A746&eid=505518CA73344221&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=9