Journal of the
Korean Mathematical Society
JKMS

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

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J. Korean Math. Soc. 2002; 39(1): 119-126

Printed January 1, 2002

Copyright © The Korean Mathematical Society.

On a central limit theorem for a stationary multivariate linear process generated by linearly positive quadrant dependent random vectors

Tae-Sung Kim

Wonkwang University

Abstract

For a stationary multivariate linear process of the form $ \mathbb{X}_{t}= {\displaystyle\sum_{j=0}^\infty} A_j \mathbb{Z}_{t-j}$, where $\{ \mathbb{Z}_t : t=0, \pm1, \pm2, \cdots \}$ is a sequence of stationary linearly positive quadrant dependent $m$-dimensional random vectors with $E(\mathbb{Z}_t)= \mathbb{O}$ and $E\|\mathbb{Z}_t \|^2 < \infty$, we prove a central limit theorem.

Keywords: multivariate linear process, linearly positive quadrant dependent random vectors, central limit theorem

MSC numbers: 60F05, 60G10