Extremes of a certain class of Gaussian processes
type: Item
instance of: scholarly article
title: Extremes of a certain class of Gaussian processes
zbMATH Open document ID: 0997.60057
DOI: 10.1016/S0304-4149(99)00041-1
published in: Stochastic Processes and their Applications
publication date: 2002-08-29T00:00:00Z
review text: The paper investigates distribution of extremes of a Gaussian process. The considered task is formulated as asymptotic behaviour of the probability \(P \{\sup _{t\geq 0}(X(t)-ct^{\beta })>u \}\) when \(u\to +\infty \). The author derives such a kind of conclusions for zero mean Gaussian processes with variance function \(t^{2H}\) fulfilling some additional conditions and \(H<\beta \). The presented results cover fractional Brownian motion and locally stationary self-similar Gaussian processes.
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60G15
zbMATH DE Number: 1792540
zbMATH Keywords: extreme values
zbMATH Keywords: Gaussian process
zbMATH Keywords: fractional Brownian motion
zbMATH Keywords: self-similar process
author: J. Hüsler
author: V. I. Piterbarg
reviewed by: Petr Lachout
MaRDI profile type: Publication
cites work: Extremes and related properties of random sequences and processes
cites work: Q4864754
description: scientific article; zbMATH DE number 1792540