Limit Theorem for High Levela-Upcrossings by $\chi$-Process

DOI10.1137/S0040585X97980786zbMath1064.60067OpenAlexW2001089526MaRDI QIDQ4830891

Siniša Stamatović, Vladimir I. Piterbarg

Publication date: 16 December 2004

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

Full work available at URL: https://doi.org/10.1137/s0040585x97980786

zbMATH Keywords

weak convergencePoisson point processmodulusupcrossingsGaussian vector process

Mathematics Subject Classification ID

Gaussian processes (60G15) Stationary stochastic processes (60G10) Limit theorems in probability theory (60F99)

Related Items (13)

High extrema of Gaussian chaos processes ⋮ Limit theorems for extremes of strongly dependent cyclo-stationary \(\chi \)-processes ⋮ Large extremes of Gaussian chaos processes ⋮ High excursions of a quadratic form for a Gaussian stationary vector process ⋮ High excursions of Bessel and related random processes ⋮ Almost sure central limit theorems for the maxima of Gaussian functions ⋮ Method of Moments for Exit Probabilities of Gaussian Vector Processes From a Large Region ⋮ Exact asymptotics and limit theorems for supremum of stationary \(\chi\)-processes over a random interval ⋮ Cox limit theorem for large excursions of a norm of a Gaussian vector process ⋮ High Extremes of Gaussian Chaos Processes: A Discrete Time Approximation Approach ⋮ On Probability of High Extremes for Product of Two Gaussian Stationary Processes ⋮ On probability of high extremes for product of two independent Gaussian stationary processes ⋮ Limit laws for the maxima of stationary chi-processes under random index

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