| 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。 |
| 《极值,正则变差和点过程(英文版)》 preface 0 preliminaries 0.1 uniform convergence 0.2 inverses of monotone functions 0.3 convergence to types theorem and limit distributions of maxima 0.4 regularly varying functions of a real variable 0.4.1 basics 0.4.2 deeper results; karamata's theorem 0.4.3 extensions of regular variation: h-variation, f-variation 1 domains of attraction and norming constants 1.1 domain of attraction of (x)= exp { - e-x } 1.2 domain of attraction of φa(x)= exp{-x-a},x ＞ 0 1.3 domain of attraction of ψa(x)= exp{-(-x)a},x ＜ 0 1.4 von mises conditions 1.5 equivalence classes and computation of normalizing constants 2 quality of convergence 2.1 moment convergence 2.2 density convergence 2.3 large deviations .2.4 uniform rates of convergence to extreme value laws 2.4.1 uniform rates of convergence to φa(x) 2.4.2 uniform rates of convergence to (x) 3 point processes 3.1 fundamentals 3.2 laplace functionals 3.3 poisson processes 3.3.1 definition and construction 3.3.2 transformations of poisson processes 3.4. vague convergence 3.5 weak convergence of point processes and random measures 4 records and extremal processes 4.1 structure of records 4.2 limit laws for records 4.3 extremal processes 4.4 weak convergence to extremal processes 4.4.1 skorohod spaces 4.4.2 weak convergence of maximal processes to extremal processes via weak convergence of induced point processes. 4.5 extreme value theory for moving averages 4.6 independence of k-record processes 5 multivariate extremes 5.1 max-infinite divisibility 5.2 an example: the bivariate normal 5.3 characterizing max-id distributions 5.4 limit distributions for multivariate extremes 5.4.1 characterizing max-stable distributions 5.4.2 domains of attraction; multivariate regular variation 5.5 independence and dependence 5.6 association references index |
内容加载中，请稍后...
商品评论（0条）