Laws of Small Numbers: Extremes and Rare Events

Second, revised and extended edition

Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss

376 pages, parution le 27/01/2005 (2^eme édition)

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Résumé

Since the publication of the first edition of this seminar book in 1994, the theory and applications of extremes and rare events have enjoyed an enormous and still increasing interest. The intention of the book is to give a mathematically oriented development of the theory of rare events underlying various applications. This characteristic of the book was strengthened in the second edition by incorporating various new results on about 130 additional pages.

Part II, which has been added in the second edition, discusses recent developments in multivariate extreme value theory. Particularly notable is a new spectral decomposition of multivariate distributions in univariate ones which makes multivariate questions more accessible in theory and practice. One of the most innovative and fruitful topics during the last decades was the introduction of generalized Pareto distributions in the univariate extreme value theory. Such a statistical modelling of extremes is now systematically developed in the multivariate framework.

The theory of rare events of non iid observations, as outlined in Part III, has seen many new approaches during the last ten years. Very often these problems can be seen as boundary crossing probabilities. Some of these new aspects of boundary crossing probabilities are dealt with in this edition.

This book is accessible to graduate students and researchers with basic knowledge in probability theory and, partly, in point processes and Gaussian processes. The required statistical prerequisites are minimal.

Sommaire

The IID Case: Functional Laws of Small Numbers
- Functional Laws of Small Numbers
- ExtremeValueTheory
- Estimation of Conditional Curves
The IID Case: Multivariate Extremes
- Basic Theory of Multivariate Maxima
- Multivariate Extremes: The Pickands Approach
- The Pickands Approach in the Bivariate Case
- Multivariate Extremes: Supplementary Concepts and Results
Non IID Observations
- Introduction to the Non IID Case
- Extremes of Random Sequences
- Extremes of Gaussian Processes
- Extensions for Rare Events
- Statistics of Extremes

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Michael Falk, Jürg Hüsler, Rolf-Dieter Reiss
Parution	27/01/2005
Édition	2^eme édition
Nb. de pages	376
Format	17 x 24
Couverture	Broché
Poids	759g
Intérieur	Noir et Blanc
EAN13	9783764324162