Titlebook: Laws of Small Numbers: Extremes and Rare Events; Michael Falk,Jürg Hüsler,Rolf-Dieter Reiss Book 2011Latest edition Springer Basel AG 2011

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Extremes of Random Sequencesnvergence of the point processes of exceedances or of clusters of exceedances. These results are then applied for special cases, as stationary, independent and particular nonstationary random sequences.

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Extremes of Gaussian Processesonary and locally stationary Gaussian processes. The asymptotic results are then applied to a statistical problem related to empirical characteristic functions. In addition, some results on other non-stationary Gaussian processes are discussed. The relation between the continuous process and its dis

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ambivalence

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Functional Laws of Small NumbersWe will develop in the following a particular extension of the well-known Poisson approximation of binomial distributions with a small hitting probability, which is known as .. This extension, which one might call .., links such seemingly different topics like non-parametric regression analysis and extreme value theory.

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Multivariate Extremes: Supplementary Concepts and ResultsIn this chapter we will deal with exceedances and upper order statistics (besides maxima), with the point process approach being central for these investigations. Extremes will be asymptotically represented by means of Poisson processes with intensity measures given by max-Lévy measures as introduced in Section 4.3.

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