Extreme Values, Regular Variation, and Point Processes (Springer Series in Operations Research and Financial Engineering)

Editorial Reviews        Review
  "This book is written in a very lucid way. The style is sober, the mathematicstone is pleasantly conversational, convincing and enthusiastic. Abeautiful book!"
  ---Bulletin of the Dutch Mathematical Society
  "Thismonograph is written in a very attractive style. It contains a lot ofcomplementary exercises and practically all important bibliographicalreference."
  ---Revue Roumaine de Mathématiques Pures et Appliquées
  

      Product Description
  Extremes Values,Regular Variation and Point Processes is a readable and efficientaccount of the fundamental mathematical and stochastic processtechniques needed to study the behavior of extreme values of phenomenabased on independent and identically distributed random variables andvectors. It presents a coherent treatment of the distributional andsample path fundamental properties of extremes and records. Itemphasizes the core primacy of three topics necessary for understandingextremes: the analytical theory of regularly varying functions; theprobabilistic theory of point processes and random measures; and thelink to asymptotic distribution approximations provided by the theoryof weak convergence of probability measures in metric spaces.
  Thebook is self-contained and requires an introductory measure-theoreticcourse in probability as a prerequisite. Almost all sections have anextensive list of exercises which extend developments in the text,offer alternate approaches, test mastery and provide for enjoyablemuscle flexing by a reader. The material is aimed at students andresearchers in probability, statistics, financial engineering,mathematics, operations research, civil engineering and economics whoneed to know about: asymptotic methods for extremes; models for recordsand record frequencies; stochastic process and point process methodsand their applications to obtaining distributional approximations;pervasive applications of the theory of regular variation inprobability theory, statistics and financial engineering.