Refinement of the almost sure central limit theorem for associated processes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

Refinement of the almost sure central limit theorem for associated processes

Authors:	M. A. Vronskii

Affiliation:	(1) M. V. Lomonosov Moscow State University, Moscow, USSR

Abstract:	In this paper, for the partial sumsS _n of a stationary associated random process it is proved that the logarithmic averages $(log n)^{ - 1} sumnolimits_{j = 1}^n {f(S_j /sqrt j )/j}$ converge almost surely. The asymptotic normality of the normalized difference between the logarithmic averages and their limiting value is established. Translated fromMatematicheskie Zametki, Vol. 68, No. 4, pp. 513–522, October, 2000.

Keywords:	associated random variables central limit theorem almost sure versions of limit theorems
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