Probability distributions of extremes of self-similar Gaussian random fields

摘要

We have obtained some upper bounds for the probability distribution ofextremes of a self-similar Gaussian random field with stationary rectangularincrements that are defined on the compact spaces. The probabilitydistributions of extremes for the normalized self-similar Gaussian randomfields with stationary rectangular increments defined in ${\mathbb{R}}^2_+$have been presented. In our work we have used the techniques developed for theself-similar fields and based on the classical series analysis of the maximalprobability bounding from below for the Gaussian fields.