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Extreme Values, Regular Variation and Point Processes

  • Sidney I. Resnick

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Sidney I. Resnick
    Pages 1-37
  3. Sidney I. Resnick
    Pages 38-75
  4. Sidney I. Resnick
    Pages 76-122
  5. Sidney I. Resnick
    Pages 123-161
  6. Sidney I. Resnick
    Pages 162-249
  7. Sidney I. Resnick
    Pages 250-306
  8. Back Matter
    Pages 307-320

About this book

Introduction

Extremes Values, Regular Variation and Point Processes is a readable and efficient account of the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It presents a coherent treatment of the distributional and sample path fundamental properties of extremes and records. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.

The book is self-contained and requires an introductory measure-theoretic course in probability as a prerequisite. Almost all sections have an extensive list of exercises which extend developments in the text, offer alternate approaches, test mastery and provide for enjoyable muscle flexing by a reader. The material is aimed at students and researchers in probability, statistics, financial engineering, mathematics, operations research, civil engineering and economics who need to know about:

* asymptotic methods for extremes;

* models for records and record frequencies;

* stochastic process and point process methods and their applications to obtaining distributional approximations;

* pervasive applications of the theory of regular variation in probability theory, statistics and financial engineering.

"This book is written in a very lucid way. The style is sober, the mathematics tone is pleasantly conversational, convincing and enthusiastic. A beautiful book!"

---Bulletin of the Dutch Mathematical Society

"This monograph is written in a very attractive style. It contains a lot of complementary exercises and practically all important bibliographical reference."

---Revue Roumaine de Mathématiques Pures et Appliquées

Keywords

Karamata's Theorem Laplace Functionals Max-Infinite Divisibility Multivariate Extremes Poisson Processes Skorohod Spaces approximation distribution Mathematica operations research point process Poisson process probability probability theory random measure Random variable statistics stochastic process stochastic processes Variation

Authors and affiliations

  • Sidney I. Resnick
    • 1
  1. 1.School of Operations Research and Industrial EngineeringCornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-75953-1
  • Copyright Information Springer Science+Business Media New York 1987
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-75952-4
  • Online ISBN 978-0-387-75953-1
  • Series Print ISSN 1431-8598
  • Series Online ISSN 2197-1773
  • Buy this book on publisher's site