Multivariate Extreme Value Theory and D-Norms
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
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Michael Falk
Multivariate Extreme Value Theory and D-Norms
Springer Series in Operations Research and Financial Engineering Series Editors Thomas V. Mikosch Sidney I. Resnick Stephen M. Robinson
More information about this series at http://www.springer.com/series/3182
Michael Falk
Multivariate Extreme Value Theory and D-Norms
123
Michael Falk Fakult¨at f¨ur Mathematik und Informatik Universit¨at W¨urzburg W¨urzburg, Germany
ISSN 1431-8598 ISSN 2197-1773 (electronic) Springer Series in Operations Research and Financial Engineering ISBN 978-3-030-03818-2 ISBN 978-3-030-03819-9 (eBook) https://doi.org/10.1007/978-3-030-03819-9 Library of Congress Control Number: 2018965201 Mathematics Subject Classification: 60E05, 60G70, 62H05 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
‘We do not want to calculate, we want to reveal structures.’ - David Hilbert, 1930 -
This book is dedicated to my teacher, Rolf Reiss. . . . you were the one who had made it so clear. . . George Harrison, All Those Years Ago
Preface
Multivariate extreme value theory (MEVT) is the appropriate toolbox for analyzing several extremal events simultaneously. However, MEVT is by no means easy to access; its key results are formulated in a measure-theoretic setup in which a common thread is not visible. Writing the ‘angular measure’ in MEVT in terms of a random vector, however, provides the missing common thread: every result in MEVT, every relevant probability distribution, be it a max-stable one or a generalized Pareto distribution, every relevant copula, every tail dependence coefficient, etc., can be formulated using a particular kind of norm on the multivariate Euclidean spa
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