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. In this third edition, the dramatic change of focus of extreme value theory has been taken into account: from concentrating on maxima of observations it has shifted to large observations, defined as exceedances over high thresholds. One emphasis of the present third edition lies on multivariate generalized Pareto distributions, their representations, properties such as their peaks-over-threshold stability, simulation, testing and estimation. Reviews of the 2nd edition: "In brief, it is clear that this will surely be a valuable resource for anyone involved in, or seeking to master, the more mathematical features of this field." David Stirzaker, Bulletin of the London Mathematical Society "Laws of Small Numbers can be highly recommended to everyone who is looking for a smooth introduction to Poisson approximations in EVT and other fields of probability theory and statistics. In particular, it offers an interesting view on multivariate EVT and on EVT for non-iid observations, which is not presented in a similar way in any other textbook." Holger Drees, Metrika

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.

These lecture notes contain a guided tour to the Novikov Conjecture and related conjectures due to Baum-Connes, Borel and Farrell-Jones. They begin with basics about higher signatures, Whitehead torsion and the s-Cobordism Theorem. Then an introduction to surgery theory and a version of the assembly map is presented. Using the solution of the Novikov conjecture for special groups some applications to the classification of low dimensional manifolds are given.

This monograph compiles the contemporary knowledge about D-norms and provides an introductory tour through the essentials of multivariate extreme value theory. Following a clear introduction of D-norms, this book introduces links with the theory through multivariate generalized Pareto distributions and max stable distributions. Further views on D-norms from a functional analysis perspective and from stochastic geometry underline the aim of this book to reveal mathematical structures. This book is intended for mathematicians with a basic knowledge of analysis and probability theory, including Fubini's theorem.

Statistical analysis of extreme data is vital to many disciplines including hydrology, insurance, finance, engineering and environmental sciences. This book provides a self-contained introduction to parametric modeling, exploratory analysis and statistical interference for extreme values. For this Third Edition, the entire text has been thoroughly updated and rearranged to meet contemporary requirements, with new sections and chapters address such topics as dependencies, the conditional analysis and the multivariate modeling of extreme data. New chapters include An Overview of Reduced-Bias Estimation; The Spectral Decomposition Methodology; About Tail Independence; and Extreme Value Statistics of Dependent Random Variables.

Mathematica combines symbolic and numerical calculations, plots, graphics programming, list calculations and structured documentation into an interactive environment. This book covers the program and shows with practical examples how even more complex problems can be solved with just a few commands. From the reviews: "A valuable introductory textbook on Mathematica and is very useful to scientists and engineers who use Mathematica in their work." -- ZENTRALBLATT MATH

Significant, and usually unwelcome, surprises, such as floods, financial crisis, epileptic seizures, or material rupture, are the topics of Extreme Events in Nature and Society. The book, authored by foremost experts in these fields, reveals unifying and distinguishing features of extreme events, including problems of understanding and modelling their origin, spatial and temporal extension, and potential impact. The chapters converge towards the difficult problem of anticipation: forecasting the event and proposing measures to moderate or prevent it. Extreme Events in Nature and Society will interest not only specialists, but also the general reader eager to learn how the multifaceted field of extreme events can be viewed as a coherent whole.