High Extremes of Gaussian Chaos Processes: A Discrete Time Approximation Approach

DOI10.1137/S0040585X97T988885zbMath1414.60024OpenAlexW2898399556WikidataQ129046490 ScholiaQ129046490MaRDI QIDQ4961761

A. I. Zhdanov, Vladimir I. Piterbarg

Publication date: 25 October 2018

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97t988885

zbMATH Keywords

Gaussian processesdouble sum methodGaussian chaoshigh extreme probabilitiesLaplace saddle point approximation method

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Extreme value theory; extremal stochastic processes (60G70)

Related Items (7)

Extremes of Gaussian chaos processes with trend ⋮ High excursions of a quadratic form for a Gaussian stationary vector process ⋮ High excursions of Bessel and related random processes ⋮ Extremes of vector-valued Gaussian processes ⋮ Method of Moments for Exit Probabilities of Gaussian Vector Processes From a Large Region ⋮ High excursions of Bessel process and other processes of Bessel type ⋮ Massive Excursions of Gaussian Isotropic Fields. Method of Moments

Cites Work

• Unnamed Item
• High extrema of Gaussian chaos processes
• On extremal behavior of Gaussian chaos
• Asymptotic expansion of Gaussian chaos via probabilistic approach
• On the asymptotic Laplace method and its application to random chaos
• High excursions for nonstationary generalized chi-square processes
• On probability of high extremes for product of two independent Gaussian stationary processes
• Limit theorems for extremes of strongly dependent cyclo-stationary \(\chi \)-processes
• Exact asymptotics and limit theorems for supremum of stationary \(\chi\)-processes over a random interval
• Discrete and continuous time extremes of Gaussian processes
• Large extremes of Gaussian chaos processes
• On Probability of High Extremes for Product of Two Gaussian Stationary Processes
• Extremes and limit theorems for difference of chi-type processes
• Extreme values and crossings for theX²-Process and Other Functions of Multidimensional Gaussian Processes, by Reliability Applications
• Limit Theorem for High Levela-Upcrossings by $\chi$-Process
• Upcrossing Probabilities for Stationary Gaussian Processes

This page was built for publication: High Extremes of Gaussian Chaos Processes: A Discrete Time Approximation Approach