On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields
- Autores
- Maltz, Alberto Leonardo
- Año de publicación
- 1999
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
Facultad de Ciencias Exactas - Materia
-
Matemática
Random fields on integer lattice
partial-sum process
Brownian motion
uniform central limit theorem
nonuniform O-mixing
metric entropy
Gibbs fields - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/139036
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On the Central Limit Theorem for Nonuniform φ-Mixing Random FieldsMaltz, Alberto LeonardoMatemáticaRandom fields on integer latticepartial-sum processBrownian motionuniform central limit theoremnonuniform O-mixingmetric entropyGibbs fieldsThe 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.Facultad de Ciencias Exactas1999info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf643-660http://sedici.unlp.edu.ar/handle/10915/139036enginfo:eu-repo/semantics/altIdentifier/issn/0894-9840info:eu-repo/semantics/altIdentifier/issn/1572-9230info:eu-repo/semantics/altIdentifier/doi/10.1023/a:1021619613916info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/4.0/Creative Commons Attribution 4.0 International (CC BY 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:31:52Zoai:sedici.unlp.edu.ar:10915/139036Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:31:52.411SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields |
| title |
On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields |
| spellingShingle |
On the Central Limit Theorem for Nonuniform φ-Mixing Random Fields Maltz, Alberto Leonardo Matemática Random fields on integer lattice partial-sum process Brownian motion uniform central limit theorem nonuniform O-mixing metric entropy Gibbs 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 |
| dc.creator.none.fl_str_mv |
Maltz, Alberto Leonardo |
| author |
Maltz, Alberto Leonardo |
| author_facet |
Maltz, Alberto Leonardo |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Matemática Random fields on integer lattice partial-sum process Brownian motion uniform central limit theorem nonuniform O-mixing metric entropy Gibbs fields |
| topic |
Matemática Random fields on integer lattice partial-sum process Brownian motion uniform central limit theorem nonuniform O-mixing metric entropy Gibbs fields |
| dc.description.none.fl_txt_mv |
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. Facultad de Ciencias Exactas |
| 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. |
| publishDate |
1999 |
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1999 |
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publishedVersion |
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http://sedici.unlp.edu.ar/handle/10915/139036 |
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eng |
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eng |
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