On Beveridge-Nelson decomposition and limit theorems for linear random fields
type: Item
instance of: scholarly article
title: On Beveridge-Nelson decomposition and limit theorems for linear random fields
zbMATH Open document ID: 1201.60026
published in: Journal of Multivariate Analysis
publication date: 2010-02-12T00:00:00Z
review text: Let \(X_t= \sum c_k\varepsilon_{t-k}\) be a linear process. The \(\varepsilon_i\) are i.i.d. random variables and \(c_k\) and \(\varepsilon_{t-k}\) correctly define the process as stationary. The sum of dependent random variables \(\sum X_t\) can be investigated using so-called Beveridge-Nelson decomposition (BND) of linear processes. Limit theorems for \(\sum X_t\) are reduced to limit theorem for \(\sum\varepsilon_t\). So it is possible to prove the law of large numbers (LLN), strong LLN (SLLN), central limit theorem (CLT) and invariance principle (IP). The BND for random fields and some properties of corresponding coefficients are formulated. The BND is directly and also indirectly applied to prove SLLN and CLT. A limit theorem for sum of \(X_{t,s}\), where \(X_{t,s}\) is a linear field and \(t\), \(s\) are elements of some increasing sequence of subsets of \(\mathbb{Z}\), is formulated.
reviewed by: Pavel Froněk
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 5669341
zbMATH Keywords: limit theorems
zbMATH Keywords: random fields
zbMATH Keywords: Beveridge-Nelson decomposition
author: V. Paulauskas
MaRDI profile type: Publication
full work available at URL: j.jmva.2009.10.001
OpenAlex ID: W2046440462
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DOI: 10.1016/J.JMVA.2009.10.001
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description: scientific article; zbMATH DE number 5669341