Titlebook: Extremes and Related Properties of Random Sequences and Processes; M. R. Leadbetter,Georg Lindgren,Holger Rootzén Book 1983 Springer-Verla

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Book 1983s-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.

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https://doi.org/10.1007/978-3-658-07291-9 result is possible for upcrossings when α < 2, it will be seen that Poisson limits may be obtained for the related concept of ε-upcrossings, defined similarly to the e-maxima of Chapter 9.Chapter 13 Extremes of Continuous Parameter Stationary Processes Our primary task in this chapter will be to di

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Convergence of the Point Process of Exceedances, and the Distribution of ,th Largest Maximaons of this theorem yield further results concerning joint distributions of kth largest values. The formal definition and simple properties of point processes which will be needed are given in the appendix.

說明

Exceedances of Levels and ,th Largest Maxima it will be shown that the exceedances take on a Poisson character as . becomes large. This leads to the limiting distributions for the kth largest values for any . rank . = 1, 2,… (the kth “extreme order statistics”) and to their limiting joint distributions.