Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Small deviations for some multi-parameter Gaussian processes


Code(s) de Classification MSC:

Résumé: We prove some general lower bounds for the probability that a multi-parameter Gaussian process has very small values. These results, when applied to a certain class of fractional Brownian sheets, yield the exact rate for their so-called small ball probability. We show by example how to use such results to compute the Hausdorff dimension of some exceptional sets determined by maximal increments.

Mots Clés: Gaussian random field ; fractional Brownian sheet ; small ball probability ; Hausdorff dimension ; exceptional set ; random fractal

Date: 2000-04-21

Prépublication numéro: PMA-586