极值，正则变分和点过程

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

《极值，正则变差，和点过程》讲述了学习独立同分布随机变量和向量的极值现象的数学背景和随机过程技巧。重在强调极值的三个重要的话题，规则变化函数的解析理论，点过程和随机测度的概率论，度量空间概率测度的若收敛的渐进分布逼近之间的联系。目次：基础；吸引域和规范常数；收敛的质量；记录和极过程；多变量极值。