The excursions of a stationary Gaussian process outside a large two-dimensional region
type: Item
instance of: scholarly article
title: The excursions of a stationary Gaussian process outside a large two-dimensional region
zbMATH Open document ID: 0979.60020
author: Robert Illsley
published in: Advances in Applied Probability
publication date: 2002-02-03T00:00:00Z
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1621397
zbMATH Keywords: multivariate Gaussian process
zbMATH Keywords: high level crossing
zbMATH Keywords: asymptotic distributions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1239/aap/999187901
OpenAlex ID: W1980184095
DOI: 10.1239/AAP/999187901
review text: The author studies a two-dimensional stationary Gaussian process \(X(t)= (X_1(t),X_2(t))\) with mean zero, covariance matrix \(R(T)\) and marginal density \(p(x).\) The asymptotic distribution of the duration of an excursion of \(X(t)\) outside star-shaped regions having a piecewise smooth boundary are studied. The asymptotic behaviour is found to depend on three cases determined by the position of the maximum of \(p(x)\) and the value of \(R'(0).\) Some generalizations of results on the asymptotic crossing rates are obtained.
reviewed by: Andriy Olenko
description: scientific article; zbMATH DE number 1621397