- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Functional central limit theorems for multivariate linear processes generated by dependent random vectors Commun. Korean Math. Soc. 2006 Vol. 21, No. 4, 779-786 Printed December 1, 2006 Mi-Hwa Ko WonKwang University Abstract : Let $\mathbb{X}_t$ be an $m$-dimensional linear process defined by $\mathbb{X}_t = \sum_{j=0}^\infty A_j$ $\mathbb{Z}_{t-j},~ t=1,2,\ldots$, where $\{\mathbb{Z}_{t}\}$ is a sequence of $m$-dimensional random vectors with mean $\textbf{0}:m\times 1$ and positive definite covariance matrix $\Gamma:m\times m$ and $\{A_j\}$ is a sequence of coefficient matrices. In this paper we give sufficient conditions so that $\sum_{t=1}^{[ns]} \mathbb{X}_t$ (properly normalized) converges weakly to Wiener measure if the corresponding result for $\sum_{t=1}^{[n s]}\mathbb{Z}_t$ is true. Keywords : functional central limit theorem, Linear process, moving average process, negatively associated, martingale difference MSC numbers : 60F05, 60G10 Downloads: Full-text PDF

 Copyright © Korean Mathematical Society. The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd