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...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
1999
|
| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/139036 |
| Aporte de: |
| Sumario: | 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. |
|---|