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Extremes and Related Properties of Random Sequences and Processes

  • Book
  • © 1983

Overview

Authors:
  1. M. R. Leadbetter

    1. Department of Statistics, The University of North Carolina, Chapel Hill, USA

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  2. Georg Lindgren

    1. Department of Mathematical Statistics, University of Lund, Lund, Sweden

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  3. Holger Rootzén

    1. Institute of Mathematical Statistics, University of Copenhagen, Copenhagen ø, Denmark

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Part of the book series: Springer Series in Statistics (SSS)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xii
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  2. Classical Theory of Extremes

    1. Front Matter

      Pages 1-2
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    2. Asymptotic Distributions of Extremes

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 3-30

    3. Exceedances of Levels and kth Largest Maxima

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 31-48

  3. Extremal Properties of Dependent Sequences

    1. Front Matter

      Pages 49-50
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    2. Maxima of Stationary Sequences

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 51-78

    3. Normal Sequences

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 79-100

    4. Convergence of the Point Process of Exceedances, and the Distribution of kth Largest Maxima

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 101-122

    5. Nonstationary, and Strongly Dependent Normal Sequences

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 123-141

  4. Extreme Values in Continuous Time

    1. Front Matter

      Pages 143-144
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    2. Basic Properties of Extremes and Level Crossings

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 145-162

    3. Maxima of Mean Square Differentiable Normal Processes

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 163-172

    4. Point Processes of Upcrossings and Local Maxima

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 173-190

    5. Sample Path Properties at Upcrossings

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 191-204

    6. Maxima and Minima and Extremal Theory for Dependent Processes

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 205-215

    7. Maxima and Crossings of Nondifferentiable Normal Processes

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 216-242

    8. Extremes of Continuous Parameter Stationary Processes

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 243-263

  5. Applications of Extreme Value Theory

    1. Front Matter

      Pages 265-265
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    2. Extreme Value Theory and Strength of Materials

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 267-277

    3. Application of Extremes and Crossings under Dependence

      • M. R. Leadbetter, Georg Lindgren, Holger Rootzén
      Pages 278-304
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Keywords

About this book

Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.

Authors and Affiliations

  • Department of Statistics, The University of North Carolina, Chapel Hill, USA

    M. R. Leadbetter

  • Department of Mathematical Statistics, University of Lund, Lund, Sweden

    Georg Lindgren

  • Institute of Mathematical Statistics, University of Copenhagen, Copenhagen ø, Denmark

    Holger Rootzén

Bibliographic Information

  • Book Title: Extremes and Related Properties of Random Sequences and Processes

  • Authors: M. R. Leadbetter, Georg Lindgren, Holger Rootzén

  • Series Title: Springer Series in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-5449-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1983

  • Softcover ISBN: 978-1-4612-5451-5Published: 10 November 2011

  • eBook ISBN: 978-1-4612-5449-2Published: 06 December 2012

  • Series ISSN: 0172-7397

  • Series E-ISSN: 2197-568X

  • Edition Number: 1

  • Number of Pages: XII, 336

  • Topics: Statistics, general, Probability Theory and Stochastic Processes

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