Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SELF-NORMALIZED WEAK LIMIT THEOREMS FOR A ø-MIXING SEQUENCE

  • Choi, Yong-Kab (DEPARTMENTS OF MATHEMATICS AND RINS GYEONGSANG NATIONAL UNIVERSITY) ;
  • Moon, Hee-Jin (DEPARTMENTS OF MATHEMATICS AND RINS GYEONGSANG NATIONAL UNIVERSITY)
  • Received : 2008.12.26
  • Published : 2010.11.30
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Abstract

Let {$X_j,\;j\geq1$} be a strictly stationary $\phi$-mixing sequence of non-degenerate random variables with $EX_1$ = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {$X_j$} under the condition that L(x) := $EX_1^2I{|X_1|{\leq}x}$ is a slowly varying function at $\infty$, without any higher moment conditions.

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References

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