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SELF-NORMALIZED WEAK LIMIT THEOREMS FOR A φ-MIXING SEQUENCE

문희진|최용갑
대한수학회 (The Korean Mathematical Society)|2010.11|대한수학회보 (Bulletin of the KMS)|제47권 제6호|pp. 1139-1153

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키워드

central limit theoreminvariance principleself-normalized random variablesmixing sequence
주제분류수학

초록

Let {Xj, j ≥ 1} be a strictly stationary φ-mixing sequence of non-degenerate random variables with EX1 = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {Xj} under the condition that L(x) := EX21 I{|X1| ≤ x} is a slowly varying function at ∞, without any higher moment conditions.

Abstract

Let {Xj, j ≥ 1} be a strictly stationary φ-mixing sequence of non-degenerate random variables with EX1 = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {Xj} under the condition that L(x) := EX21 I{|X1| ≤ x} is a slowly varying function at ∞, without any higher moment conditions.

참고문헌 (16)

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