Laws of Small Numbers: Extremes and Rare Events / Edition 2

Laws of Small Numbers: Extremes and Rare Events / Edition 2

by Michael Falk
     
 

ISBN-10: 3764324163

ISBN-13: 9783764324162

Pub. Date: 09/11/2008

Publisher: Springer-Verlag New York, LLC

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

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Overview

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.

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Product Details

ISBN-13:
9783764324162
Publisher:
Springer-Verlag New York, LLC
Publication date:
09/11/2008
Edition description:
REV
Pages:
396
Product dimensions:
9.21(w) x 6.14(h) x 0.81(d)

Table of Contents

Pt. IThe IID case : functional laws of small numbers1
1Functional laws of small numbers3
2Extreme value theory23
3Estimation of conditional curves75
Pt. IIThe IID case : multivariate extremes105
4Basic theory of multivariate maxima107
5Multivariate extremes : the Pickands approach131
6The Pickands approach in the bivariate case161
7Multivariate extremes : supplementary concepts and results203
Pt. IIINon IID observations233
8Introduction to the non IID case235
9Extremes of random sequences249
10Extremes of gaussian processes273
11Extensions for rare events297
12Statistics of extremes329

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