대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제29권2호
  • /
  • Pages.351-358
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  • 2014
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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THE LIMIT THEOREMS UNDER LOGARITHMIC AVERAGES FOR MIXING RANDOM VARIABLES

  • Zhang, Yong (College of Mathematics Jilin University)
  • 투고 : 2013.05.09
  • 발행 : 2014.04.30
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초록

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

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참고문헌

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