Point processes of exits by bivariate Gaussian processes and extremal theory for the \(\chi^2\)-process and its concomitants

DOI10.1016/0047-259X(80)90013-5zbMath0425.60030MaRDI QIDQ1135573

Georg Lindgren

Publication date: 1980

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

reliabilitycrossingsmaximaextremal theoryconvergence of point processesbivariate Gaussian processes

Mathematics Subject Classification ID

Gaussian processes (60G15) Stationary stochastic processes (60G10) Sample path properties (60G17) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (8)

High excursions for nonstationary generalized chi-square processes ⋮ Extremes of L^p-norm of vector-valued Gaussian processes with trend ⋮ Extremes and crossings for differentiable stationary processes with application to Gaussian processes in \(\mathbb{R}{}^ m\) and Hilbert space ⋮ On the general law of iterated logarithm with application to selfsimilar processes and to Gaussian processes in \(\mathbb{R}{}^ n\) and Hilbert space ⋮ Sojourns of vector Gaussian processes inside and outside spheres ⋮ Extremal ranks and transformation of variables for extremes of functions of multivariate Gaussian processes ⋮ Gaussian stochastic processes ⋮ Piterbarg theorems for chi-processes with trend

Cites Work

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• Weak convergence of high level crossings and maxima for one or more Gaussian processes
• Weak convergence results for extremal processes generated by dependent random variables
• A note on the asymptotic independence of high level crossings for dependent Gaussian processes
• On the joint distribution of crossings of high multiple levels by a stationary Gaussian process
• Extreme values and crossings for theX²-Process and Other Functions of Multidimensional Gaussian Processes, by Reliability Applications
• Some properties of the crossings process generated by a stationary χ² process
• Asymptotic Independence of the Numbers of High and Low Level Crossings of Stationary Gaussian Processes
• On extreme values in stationary sequences

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