| Document Type
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BL
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| Record Number
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860165
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| Main Entry
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Falk, Michael,1954-
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| Title & Author
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Multivariate extreme value theory and d-norms /\ Michael Falk.
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| Publication Statement
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Cham, Switzerland :: Springer,, 2019.
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| Series Statement
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Springer series in operations research and financial engineering,
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| Page. NO
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1 online resource (x, 241 pages) :: illustrations
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| ISBN
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303003819X
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: 3030038203
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: 9783030038199
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: 9783030038205
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3030038181
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9783030038182
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; Contents; 1 D-Norms; 1.1 Norms and D-Norms; 1.2 Examples of D-Norms; 1.3 Takahashi's Characterizations; 1.4 Convexity of the Set of D-Norms; 1.5 When Is an Arbitrary Norm a D-Norm?; 1.6 The Dual D-Norm Function; 1.7 Normed Generators Theorem; 1.8 Metrization of the Space of D-Norms; 1.9 Multiplication of D-Norms; 1.10 The Functional D-Norm; 1.11 D-Norms from a Functional Analysis Perspective; Introducing the Relevant Space of Seminorms; 1.12 D-Norms from a Stochastic Geometry Perspective; 2 D-Norms & Multivariate Extremes; 2.1 Univariate Extreme Value Theory
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2.2 Multivariate Generalized Pareto DistributionsGeneral Multivariate GPDS; 2.3 Multivariate Max-Stable Distributions; 2.4 How to Generate Max-Stable RVS; 2.5 Covariances, Range, etc. of Standard Max-Stable rvs; 2.6 Max-Stable Random Vectors as Generators of D-Norms; 3 Copulas & Multivariate Extremes; 3.1 Characterizing Multivariate Domain of Attraction; 3.2 Multivariate Piecing-Together; 3.3 Copulas Not in the Domain of Attraction; 4 An Introduction to Functional Extreme Value Theory; 4.1 Generalized Pareto Processes; Defining a Simple Generalized Pareto Process; 4.2 Max-Stable Processes
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4.3 Generalized Max-Linear Models5 Further Applications of D-Norms to Probability & Statistics; 5.1 Max-Characteristic Function; 5.2 Multivariate Order Statistics: The Intermediate Case; 5.3 Multivariate Records and Champions; Simple Records; References; Index
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| Abstract
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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.
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| Subject
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Multivariate analysis.
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| Subject
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Multivariate analysis.
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| Dewey Classification
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519.5/35
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| LC Classification
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QA278
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