Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2000; 37(3): 463-471

Printed May 1, 2000

Copyright © The Korean Mathematical Society.

A central limit theorem for the stationary linear process generated by an associated process

Tae-Sung Kim, Jong-Il Baek, and Jae-Hak Lim

Wonkwang University, Wonkwang University, Taejon National University of Technology

Abstract

A central limit theorem is obtained for stationary linear process $X_{t}= \sum_{j=0}^\infty a_j \epsilon_{t-j}$, where $\{\epsilon_t \}$ is a strictly stationary associated sequence with $E\epsilon_t =0,~E \epsilon_t^2 < \infty.$ A functional central limit theorem is also derived.

Keywords: central limit theorem, associated, linear process, stationary, maximal inequality for associated sequence

MSC numbers: 60G10