On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields

Alberto L. Maltz ()
Additional contact information
Alberto L. Maltz: Universidad Nacional de La Plata

Journal of Theoretical Probability, 1999, vol. 12, issue 3, 643-660

Abstract: Abstract The partial-sum processes, indexed by sets, of a stationary nonuniform φ-mixing random field on the d-dimensional integer lattice are considered. A moment inequality is given from which the convergence of the finite-dimensional distributions to a Brownian motion on the Borel subsets of [0, 1] d is obtained. A Uniform CLT is proved for classes of sets with a metric entropy restriction and applied to certain Gibbs fields. This extends some results of Chen(5) for rectangles. In this case and when the variables are bounded a simpler proof of the uniform CLT is given.

Keywords: Random fields on integer lattice; partial-sum process; Brownian motion; uniform central limit theorem; nonuniform φ-mixing; metric entropy; Gibbs fields (search for similar items in EconPapers)
Date: 1999
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1023/A:1021619613916 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:12:y:1999:i:3:d:10.1023_a:1021619613916

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1021619613916

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().