概率统计中的极限理论及其应用

出版时间：2007-1  出版社：高等教育出版社  作者：黎子良，钱莲芬，邵启满　编  页数：533  字数：540000  

前言

To celebrate the 65th birthday of Professor Zhengyan Lin, an Inter-national Conference on Asymptotic Theory in Probability and Statisticswas held at the Center of Mathematical Sciences and Department ofMathematics of Zhejiang University, Hangzhou, China, in the summerof 2006. One of the aims of the conference was to provide a platformfor the exchange of new ideas and recent developments in asymptotictheory and applications. Many speakers of the conference were invitedto contribute to this volume, which consists of expository papers basedon their invited talks or related research areas. All papers were carefullypeer refereed. We would like to dedicate this book to Professor ZhengyanLin and wish him continuing success in many years to come!Professor Lin is a leading probabilist in China. He has made sig-nificant contributions to the development of asymptotic theory, espe-cially, limit theorems for mixing dependent random variables and self-normalized sums, and sample path properties of Gaussian processes.Professor Lin has published over 140 papers and 7 books.  He andProfessor Chuanrong Lu have supervised over 160 graduate students atHangzhou University (now merged with Zhejiang University) since 1982.An objective of the present volume of 18 papers by the invited speak-ers and contributors to the conference is to introduce graduate studentsto some active research areas in probability and statistics. Most papersare survey papers so that the present volume can provide readers witha valuable resource in probability, statistics and their applications. Ob-viously, we cannot cover all of the important topics of current research.The volume consists of three parts: (I) Limit Theorems, (II) Statisticsand Applications, and (III) Mathematical Finance and Insurance.Part I has 8 papers, focusing on limit theory through various angles.It starts with the probability theory of self-normalization (Lai and Shao),followed by random partitions (Su), adaptive designs (Zhang), Gaussianprocesses (Wang), Gaussian random fields (Xiao), large deviations the-ory for two-parameter Gaussian processes (Chen and CsSrgS), intersec-tion local times (Chen), and ends with limit theorems for U-statistics(JING) to serve as a link between probability and statistics.

内容概要

This volume is a collection of 18 papers on asymptotic theory in probability, statistics and their applications to a wide variety of problems.It contains three parts, limit theorems, statistics and applications, mathematical finance and Insurance.Most papers are survey papers and the volume is intended for graduate students in probability and statistics and researchers in related areas.

书籍目录

Part Ⅰ: Limit Theorems.　Self-normalized Limit Theorems in Probability and Statistics　Asymptotic Analysis of Random Partitions　Limit Theorems on Adaptive Designs in Clinical Trials　Functional Limit Theorems for Gaussian Processes　Strong Local Nondeterminism and Sample Path Properties of Gaussian Random Fields　Large Deviations for Two-Parameter Gaussian Processes Related to Change-Point Analysis　Intersection Local Times: Large Deviations and Laws of the Iterated Logarithm　Limit Theorems for U-StatisticsPart Ⅱ: Statistics and Applications　On the Inverse Problem for the t-Statistic　Statistical Analysis for Rounded Data　Piecewise Regression Models: Estimation Theory and Applications　Estimation in Partially Linear Models With Missing Data: A Review　Asymptotic Methods in Nonlinear Time Series Models　Nonparametric Classification and Probabilistic Classifier with Environmental and Remote Sensing 　Applications　Mixed Linear Model Approaches for Complex Trait AnalysisPart Ⅲ: Mathematical Finance and Insurance　Inference and Computation for Stochastic Volatility Models Related to Option Pricing　A Selective Overview of Applications of Choquet Integrals　Some Recent Developments in Actuarial Science

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《概率统计中的极限理论及其应用(英文版)》由高等教育出版社出版。The launch of this Advanced Lectures in Mathematics series is aimed at keepingmathematicians informed of the latest developments in mathematics, as well asto aid in the learning of new mathematical topics by students all over the world.Each volume consists of either an expository monograph or a collection of significant introductions to important topics. This series emphasizes the history andsources of motivation for the topics under discussion, and also gives an overviewof the current status of research in each particular field. These volumes are thefirst source to which people will turn in order to learn new subjects and to discover the latest results of many cutting-edge fields in mathematics.