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.

Provides an easy access to multivariate extreme value theory Compiles the contemporary knowledge about D-norms Provides a relaxed tour through the essentials of multivariate extreme value theory Develops the notion of D-Norm as a convenient tool to represent the multivariate extreme value laws of max-stable processes

Autorentext
Prof. Dr. Michael Falk, Universität Würzburg, Institut für Mathematik VIII - Statistik Dipl. Math. Johannes Hain, Universität Würzburg, Institut für Mathematik VIII - Statistik Prof. Dr. Frank Marohn, Universität Würzburg, Institut für Mathematik VIII - Statistik Dr. Hans Fischer, Katholische Universität Eichstätt-Ingolstadt Mathematisch-Geographische Fakultät, Didaktik der Mathematik

Klappentext

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.

Inhalt

1. D-Norms.- 2. D-Norms & Multivariate Extremes.- 3. Copulas & Multivariate Extremes.- 4. An Introduction to Functional Extreme Value Theory.- 5. Further Applications of D-Norms to Probability & Statistics.