極值,正則變差和點過程(英文版)

內(nèi)容概要

　　本書講述了學習獨立同分布隨機變量和向量的極值現(xiàn)象的數(shù)學背景和隨機過程技巧。重在強調(diào)極值的三個重要的話題，規(guī)則變化函數(shù)的解析理論，點過程和隨機測度的概率論，度量空間概率測度的若收斂的漸進分布逼近之間的聯(lián)系。目次：基礎；吸引域和規(guī)范常數(shù)；收斂的質(zhì)量；記錄和極過程；多變量極值。

書籍目錄

Preface
Preliminaries
Uniform Convergence
Inverses of Monotone Functions
Convergence to Types Theorem and Limit Distributions of
Maxima
Regularly Varying Functions of a Real Variable Basics
Deeper Results；Karamata’S Theorem
Extensions of Regular Variation：兀．Variation．F．Variation
Domains ofAttraction and Norming Constants
Domain ofAttraction ofA(x)=exp
Domain ofAttraction
Domain ofAttraction
Von Mises Conditions
Equivalence Classes and Computation of Normalizing Constants
Quality ofConvergence
Moment Convergence
Density Convergence
Large Deviations．
Uniform Rates of Convergence to Extreme Value Laws
Uniform Rates of Convergence
Uniform Rates of Convergence
Point Processes
Fundamentals
Laplace Functionals
Poisson Processes
Definition and Construction
Transformations of Poisson Processes
Vague Convergence
Weak Convergence of Point Processes and Random Measures
Records and Extrema Processes
Structure of Records
Limit Laws for Records
Extremal Processes
Weak Convergence to Extremal Processes Skorohod Spaces
Weak Convergence of Maximal Processes to Extremal
Processes via Weak Convergence of Induced Point Processes
Extreme Value Theory for Moving Averages
Independence of k-Record Processes
Multivariate Extremes
Max．Infinite Divisibility
An Example：The Bivariate Normal
Characterizing Max．id Distributions
Limit Distributions for Multivariate Extremes
Characterizing Max．Stable Distributions
Domains of Attraction；Multivariate Regular Variation
Independence and Dependence
Association
Refe
Inde

章節(jié)摘錄

　　Extreme value theory is an elegant and mathematically fascinating theory aswell as a subject which pervades an enormous variety of applications.Considerthe following circumstances：Air pollution monitoring stations are located at various sites about a city.Government regulations mandate that pollution cOncentratiOns measuredat each site be below certain specified levels.A skyscraper iS to be built near Lake Michigan and thus will be subject towind stresses from several directions.Design strength must be SHfficientto withstand these winds.Similarly.a mechanical component such as anairplane wing must be designed to withstand stresses from several sources.Dams or dikes at locations along a body of Water such as a river or sea mustbe built high enough to exceed the maximum water height.A mining company drills core samples at points of a grid in a given region.Continued drilling will take place in the direction of maximum ore con.centration.Athletic records are frequently broken.A common feature of these situations iS that observatiOnal data has beenor can be collected and the features of the observations ofmost interest dependon largest or smallest values；i…e on the extremes.The data must be modeledand decisions made on the basis of how one believes the extreme values willbehave.This book iS primarily concerned with the behavior of extreme values ofindependent，identically distributed fiidl observations.Within the iid frame.work there are surprising depth，beauty，and applicability.The treatment inthis book iS organized around two themes.The first iS that the central analytictool of extreme value theory is the theory of regularly varying functions，andthe second iS that the central probabilistic tool iS point process theory andin particular the Poisson process.Accordingly we have presented a carefulexposition of those aspects of regular variation and point processes which areessential for a proper understanding of extreme value theory. 　　……

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