On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields
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 ob...
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Formato: | Articulo |
Lenguaje: | Inglés |
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1999
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Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/139036 |
Aporte de: |
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I19-R120-10915-139036 |
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institution |
Universidad Nacional de La Plata |
institution_str |
I-19 |
repository_str |
R-120 |
collection |
SEDICI (UNLP) |
language |
Inglés |
topic |
Matemática Random fields on integer lattice partial-sum process Brownian motion uniform central limit theorem nonuniform O-mixing metric entropy Gibbs fields |
spellingShingle |
Matemática Random fields on integer lattice partial-sum process Brownian motion uniform central limit theorem nonuniform O-mixing metric entropy Gibbs fields Maltz, Alberto Leonardo On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields |
topic_facet |
Matemática Random fields on integer lattice partial-sum process Brownian motion uniform central limit theorem nonuniform O-mixing metric entropy Gibbs fields |
description |
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. |
format |
Articulo Articulo |
author |
Maltz, Alberto Leonardo |
author_facet |
Maltz, Alberto Leonardo |
author_sort |
Maltz, Alberto Leonardo |
title |
On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields |
title_short |
On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields |
title_full |
On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields |
title_fullStr |
On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields |
title_full_unstemmed |
On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields |
title_sort |
on the central limit theorem for nonuniform φ-mixing random fields |
publishDate |
1999 |
url |
http://sedici.unlp.edu.ar/handle/10915/139036 |
work_keys_str_mv |
AT maltzalbertoleonardo onthecentrallimittheoremfornonuniformphmixingrandomfields |
bdutipo_str |
Repositorios |
_version_ |
1764820456915861505 |