On the upper and lower classes for a stationary Gaussian stochastic process
type: Item
instance of: scholarly article
title: On the upper and lower classes for a stationary Gaussian stochastic process
zbMATH Open document ID: 0803.60028
author: J. M. P. Albin
published in: The Annals of Probability
publication date: 1995-01-03T00:00:00Z
review text: Real stationary standardized Gaussian random fields (r.f.s) \(\xi(t, \omega)\) on a pseudometric unbounded space \((T,\rho)\) are considered under some rather mild conditions on the correlation function. An integral criterion is obtained for the zero-one law of the set \[ \{\omega: \text{ the set } \{t\in T:\;\xi(t,\omega)> \psi(t)\} \text{ is \(\rho\)-unbounded}\} \] when the function \(\psi: T\to [-\infty, +\infty]\) is not required to be monotone. In particular, the r.f.s of this type and the Brownian sheet are discussed when \(T= R^ n\) and two examples of r.f.s with \(T\) non-Euclidean are presented.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F20
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G15
Mathematics Subject Classification ID: 60G17
zbMATH DE Number: 567174
zbMATH Keywords: upper and lower classes
zbMATH Keywords: entropy
zbMATH Keywords: Gaussian random fields
zbMATH Keywords: pseudometric unbounded spaces
zbMATH Keywords: Brownian sheet
reviewed by: Nijolė Kalinauskaitė
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176988848
OpenAlex ID: W2010484572
DOI: 10.1214/AOP/1176988848
description: scientific article; zbMATH DE number 567174