| Título: | Random Gaussian Sums on Trees |
| Autores: |
Lifshits, Mikhail; St. Petersburg State University Linde, Werner; FSU Jena |
| Fecha: | 2011-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Gaussian processes, processes indexed by trees, bounded processes, summation on trees, metric entropy 60G15; 06A06,; 05C05 |
| Descripción: | Let $T$ be a tree with induced partial order. We investigate a centered Gaussian process $X$ indexed by $T$ and generated by weight functions. In a first part we treat general trees and weights and derive necessary and sufficient conditions for the a.s. boundedness of $X$ in terms of compactness properties of $(T,d)$. Here $d$ is a special metric defined by the weights, which, in general, is not comparable with the Dudley metric generated by $X$. In a second part we investigate the boundedness of $X$ for the binary tree. Assuming some mild regularity assumptions about on weight, we completely characterize homogeneous weights with $X$ being a.s. bounded. |
| Idioma: | No aplica |
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