Asymptotic expansion of Gaussian chaos via probabilistic approach

DOI10.1007/s10687-015-0215-3zbMath1337.60031arXiv1307.5857OpenAlexW2006424859MaRDI QIDQ497481

Vladimir I. Piterbarg, Enkelejd Hashorva, Dmitrii Korshunov

Publication date: 24 September 2015

Published in: Extremes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1307.5857

zbMATH Keywords

asymptotic expansionrandom matricesdeterminantsmultidimensional normal distributionWiener chaossubexponential distributionpolynomial chaosGaussian chaosGaussian orthogonal ensemblemax-domain of attractionrandom Gaussian clouds

Mathematics Subject Classification ID

Gaussian processes (60G15) Random matrices (probabilistic aspects) (60B20) Extreme value theory; extremal stochastic processes (60G70) Probability distributions: general theory (60E05) Large deviations (60F10) Multiplicative functionals and Markov processes (60J57)

Related Items (15)

Extremes of Gaussian fields with a smooth random variance ⋮ High extrema of Gaussian chaos processes ⋮ Large extremes of Gaussian chaos processes ⋮ Extremes of Gaussian chaos processes with trend ⋮ Multidimensional Watson lemma and its applications ⋮ Asymptotic expansions for bivariate normal extremes ⋮ Extremes of randomly scaled Gumbel risks ⋮ High excursions of a quadratic form for a Gaussian stationary vector process ⋮ Extremes and limit theorems for difference of chi-type processes ⋮ Method of Moments for Exit Probabilities of Gaussian Vector Processes From a Large Region ⋮ On probability of high extremes of Gaussian fields with a smooth random trend ⋮ Computation and analysis of the asymptotic expansions of the compound means ⋮ An Erdős-Révész type law of the iterated logarithm for order statistics of a stationary Gaussian process ⋮ High Extremes of Gaussian Chaos Processes: A Discrete Time Approximation Approach ⋮ On the asymptotic Laplace method and its application to random chaos

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On extremal behavior of Gaussian chaos
• On the infinite sums of deflated Gaussian products
• Extremes of aggregated Dirichlet risks
• Asymptotics of supremum distribution of a Gaussian process over a Weibullian time
• Asymptotic distribution of the normal sample range
• A formula for the tail probability of a multivariate normal distribution and its applications
• Estimates of moments and tails of Gaussian chaoses
• Exact tail asymptotics in bivariate scale mixture models
• Tail behaviour of multiple random integrals and \(U\)-statistics
• Inverse problems for regular variation of linear filters, a cancellation property for \(\sigma\)-finite measures and identification of stable laws
• A ratio limit theorem for the tails of weighted sums
• Extremes of moving averages of random variables from the domain of attraction of the double exponential distribution
• On decoupling, series expansions, and tail behavior of chaos processes
• Subexponentiality of the product of independent random variables
• High excursions for nonstationary generalized chi-square processes
• A geometric approach to an asymptotic expansion for large deviation probabilities of Gaussian random vectors
• Asymptotics of the norm of elliptical random vectors
• On a multivariate version of Bernstein's inequality
• An Introduction to Heavy-Tailed and Subexponential Distributions
• Moments of the Gaussian Chaos
• An Introduction to Random Matrices
• Zum asymptotischen Verhalten der Verteilungen und der Dichten gewisser Funktionale Gauss'scher Zufallsvektoren
• Concerning a Certain Probability Problem
• Tail probabilities for weighted sums of products of normal random variables
• Densities with Gaussian Tails
• Gaussian Hilbert Spaces
• Tail and moment estimates for some types of chaos
• A Bound on Tail Probabilities for Quadratic Forms in Independent Random Variables

This page was built for publication: Asymptotic expansion of Gaussian chaos via probabilistic approach