A Nonclassical Law of the Iterated Logarithm for Functions of Positively Associated Random Variables期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A Nonclassical Law of the Iterated Logarithm for Functions of Positively Associated Random Variables

Authors:

Affiliation:

(1) Department of Statistics and Computing Science, Zhejiang Gongshang University, Hangzhou, 310035, P.R. China;(2) Department of Mathematics, Zhejiang Unviersity, Xixi Campus, Hangzhou, 310028, P.R. China

Abstract:

Let ${X_{n}; ngeq 1}$ be a sequence of stationary positively associated random variables and a sequence of positive constants $${b(n); ngeq1}$$

be monotonically approaching infinity and be not asymptotically equivalent to loglog n. Under some suitable conditions, a nonclassical law of the iterated logarithm is investigated, i.e.

$limsup_{nrightarrowinfty}frac{sum_{i=1}^{n}[f(X_{i})-E f(X_{i})]}{sqrt{2nb(n)}}=sigma_{f}hspace{0.3cm} a.s.,$

where (f) is a real function and $sigma_{f}^{2}=Var(f(X_{1}))+2sum_{j=2}^{infty}Cov(f(X_{1}), f(X_{j}))$ .

Keywords:

A nonclassical law of the iterated logarithm Positive association

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