Limit distributions for the maxima of stationary Gaussian processes

DOI10.1016/0304-4149(75)90002-2zbMath0296.60021OpenAlexW2040243058MaRDI QIDQ1213690

Donald Ylvisaker, Yash Mittal

Publication date: 1975

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0304-4149(75)90002-2

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stationary stochastic processes (60G10) Limit theorems in probability theory (60F99)

Related Items

Asymptotics of maxima and sums for a type of strongly dependent isotropic Gaussian random fields ⋮ Convergence of exceedance point processes of normal sequences with a seasonal component and its applications ⋮ Limit results for maxima in non-stationary multivariate Gaussian sequences ⋮ Exact tail asymptotics of the supremum of strongly dependent Gaussian processes over a random interval ⋮ Limit distribution of the sum and maximum from multivariate Gaussian sequences ⋮ Maxima and minima of homogeneous Gaussian random fields over continuous time and uniform grids ⋮ Asymptotic distributions of maxima of complete and incomplete samples from multivariate stationary Gaussian sequences ⋮ On the maxima and sums of homogeneous Gaussian random fields ⋮ On Piterbarg theorem for maxima of stationary Gaussian sequences ⋮ Asymptotic distributions of maxima of complete and incomplete samples from strongly dependent stationary Gaussian sequences ⋮ Extreme value theory for stochastic processes ⋮ Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays ⋮ Almost sure convergence for the maxima and minima of strongly dependent nonstationary multivariate Gaussian sequences ⋮ The maxima and sums of multivariate non-stationary Gaussian sequences ⋮ The asymptotic relation between the first crossing point and the last exit time of Gaussian order statistics sequences ⋮ The almost sure limit theorem for the maxima and minima of strongly dependent Gaussian vector sequences ⋮ Limiting distributions and almost sure limit theorems for the normalized maxima of complete and incomplete samples from Gaussian sequence ⋮ Limit distribution of maxima of strongly dependent Gaussian vector sequences under complete and incomplete samples ⋮ On Piterbarg max-discretisation theorem for standardised maximum of stationary Gaussian processes ⋮ Exact asymptotics and limit theorems for supremum of stationary \(\chi\)-processes over a random interval ⋮ Asymptotic expansions in the Poisson limit theorem for large excursions of stationary Gaussian sequences ⋮ The limit theorems for maxima of stationary Gaussian processes with random index ⋮ Asymptotics of Maxima of Strongly Dependent Gaussian Processes ⋮ Maxima and near-maxima of a Gaussian random assignment field ⋮ Joint limit distributions of exceedances point processes and partial sums of Gaussian vector sequence ⋮ On Piterbarg's max-discretisation theorem for multivariate stationary Gaussian processes ⋮ On maxima of chi-processes over threshold dependent grids ⋮ Mixture results for extremal behaviour of strongly dependent nonstationary Gaussian sequences ⋮ Limit properties of exceedance point processes of strongly dependent normal sequences ⋮ High level sojourns for strongly dependent Gaussian processes ⋮ Limit laws on extremes of nonhomogeneous Gaussian random fields ⋮ On limit distributions of first crossing points of Gaussian sequences ⋮ Directional phantom distribution functions for stationary random fields ⋮ Conditions for the convergence in distribution of maxima of stationary normal processes ⋮ Almost sure limiting behaviour of first crossing points of Gaussian sequences ⋮ Joint behavior of point process of exceedances and partial sum from a Gaussian sequence ⋮ The extremes of a triangular array of normal random variables ⋮ The limit properties of point processes of upcrossings in nonstationary strongly dependent Gaussian models ⋮ Extremal theory for long range dependent infinitely divisible processes ⋮ Comparison Inequalities for Order Statistics of Gaussian Arrays ⋮ Gaussian stochastic processes ⋮ Second-order expansion for the maximum of some stationary Gaussian sequences. ⋮ Limit laws for the maxima of stationary chi-processes under random index ⋮ Piterbarg's max-discretization theorem for stationary vector Gaussian processes observed on different grids ⋮ On Piterbarg's max-discretisation theorem for homogeneous Gaussian random fields ⋮ The dependence of extreme values of discrete and continuous time strongly dependent Gaussian processes ⋮ Maxima and sum for discrete and continuous time Gaussian processes ⋮ Asymptotic approximation of crossing probabilities of random sequences

Cites Work

• Limiting behavior of maxima in stationary Gaussian sequences
• Sur la distribution limite du terme maximum d'une série aléatoire
• Maxima of stationary Gaussian processes
• Upcrossing Probabilities for Stationary Gaussian Processes
• Asymptotic Properties of the Maximum in a Stationary Gaussian Process
• An Asymptotic 0-1 Behavior of Gaussian Processes
• Limit Theorems for the Maximum Term in Stationary Sequences
• Extreme Values in Samples from $m$-Dependent Stationary Stochastic Processes