THE LIMIT THEOREMS UNDER LOGARITHMIC AVERAGES FOR MIXING RANDOM VARIABLES

Title & Authors
THE LIMIT THEOREMS UNDER LOGARITHMIC AVERAGES FOR MIXING RANDOM VARIABLES
Zhang, Yong;

Abstract
In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for $\small{\sum_{k{\leq}N}k^{-1}f(S_k/{\sigma}\sqrt{k})}$, where $\small{S_k}$ is the partial sums of strictly stationary mixing random variables with $\small{EX_1=0}$ and $\small{{\sigma}^2=EX^2_1+2\sum_{k=1}^{\infty}EX_1X_{1+k}}$. We also establish an almost sure limit behaviors of the above sums.
Keywords
central limit theorem;almost sure central limit theorem;logarithmic averages;mixing random variables;
Language
English
Cited by
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