概率论7
随机微分方程 豆瓣
作者: 科森多尔 出版社: 北京世界图书出版公司 2006 - 11
《随机微分方程》(第6版)是《Universitext》丛书之一,是一部理想的研究生教材,内容做了较大的修改和补充,包括鞅表示论、变分不等式和随机控制等内容,书后附有部分习题解答和提示。随机微分方程在数学以外的许多领域有着广泛的应用,它对数学领域中的许多分支起着有效的联结作用。
实验设计与分析 豆瓣
作者: (美)蒙哥马利(Montgomery,D.C) 译者: 傅钰生等 出版社: 人民邮电出版社 2009 - 1
本书作为实验设计与分析领域的名著, 是作者在亚利桑那州立大学、华盛顿大学和佐治亚理工学院三所大学近40年实验设计教学经验的基础上编写的. 全书内容广泛, 实例丰富,包括简单比较试验、析因设计、分式析因第1章设计、拟合回归模型、响应曲面方法和设计、稳健参数设计和过程稳健性研究、含随机因子的实验、嵌套设计和裂区设计等.
本书可作为自然科学研究人员、工程技术人员、管理人员进行科学实验设计与分析的参考书, 也可作为农林类、医学类、生物类、统计类的教师和高年级本科生和研究生的教学参考用书.
遍历性理论引论 豆瓣
作者: P.Walters 出版社: 世界图书出版公司 2003 - 6
In 1970 I gave a graduate course in ergodic theory at the University of Maryland in College Park, and these lectures were the basis of the Springer Lecture Notes in Mathematics Volume 458 called "Ergodic Theory--Introductory Lectures" which was published in 1975. This volume is nowout of print, so I decided to revise and add to the contents of these notes. I have updated the earlier chapters and have added some new chapters on the ergodic theory of continuous transformations of compact metric spaces. In particular, I have included some material on topological pressure and equilibrium states. In recent years there have been some fascinating interactions of ergodic theory with differentiable dynamics, differential geometry,number theory, von Neumann algebras, probability theory, statistical mechanics, and other topics. In Chapter 10 1 have briefly described some of these and given references to some of the others. I hope that this book will give the reader enough foundation to tackle the research papers on ergodictheory and its applications.
概率论与随机过程中的泛函分析(影印版) 豆瓣
作者: 博布罗斯基 出版社: 高等教育出版社 2008 - 3
本书主要包含国外反映近代数学发展的纯数学与应用数学方面的优秀书籍,天元基金邀请国内各个方向的知名数学家参与选题的工作,经专家遴选、推荐而出版。
目录
Preface
1 Preliminaries, notations and conventions
1.1 Elements of topology
1.2 Measure theory
1.3 Functions of bounded variation. Riemann-Stieltjes integral
1.4 Sequences of independent random variables
1.5 Convex functions. Holder and Minkowski inequalities
1.6 The Cauchy equation
2 Basic notions in functional analysis
2.1 Linear spaces
2.2 Banach spaces
2.3 The space of bounded linear operators
3 Conditional expectation
3.1 Projections in Hilbert spaces
3.2 Definition and existence of conditional expectation
3.3 Properties and examples
3.4 The Radon-Nikodym Theorem
3.5 Examples of discrete martingales
3.6 Convergence of self-adjoint operators
3.7 ... and of martingales
4 Brownian motion and l-Iilbert spaces
4.1 Gaussian families & the definition of Brownian motion
4.2 Complete orthonormal sequences in a Hilbert space
4.3 Construction and basic properties of Brownian motion
4.4 Stochastic integrals
5 Dual spaces and convergence of probability measures
5.1 The Hahn-Banach Theorem
5.2 Form of linear functionals in specific Banach spaces
5.3 Thedual of an operator
5.4 Weak and weak* topologies
5.5 The Central Limit Theorem
5.6 Weak convergence in metric spaces
5.7 Compactness everywhere
5.8 Notes on other modes of convergence
6 The Gelfand transform and its applications
6.1 Banach algebras
6.2 The Gelfand transform
6.3 Examples of Gelfand transform
6.4 Examples of explicit calculations of Gelfand transform
6.5 Dense subalgebras of C(S)
6.6 Inverting the abstract Fourier transform
6.7 The Factorization Theorem
7 Semigroups of operators and Levy processes
7.1 The Banach-Steinhaus Theorem
7.2 Calculus of Banach space valued functions
7.3 Closed operators
7.4 Semigroups of operators
7.5 Brownian motion and Poisson process semigroups
7.6 More convolution semigroups
7.7 The telegraph process semigroup
7.8 Convolution semigroups of measures on semigroups
8 Markov processes and semigroups of operators
8.1 Semigroups of operators related to Markov processes
8.2 The Hille-Yosida Theorem
8.3 Generators of stochastic processes
8.4 Approximation theorems
9 Appendixes
9.1 Bibliographical notes
9.2 Solutions and hints to exercises
9.3 Some commonly used notations
References
Index
概率与测度 豆瓣
作者: 别林斯里 出版社: 世界图书出版公司 2007 - 5
《概率与测度(第3版)》是《概率与测度》第3版,新版保留了原先的风格,将测度论和概率论有机结合在一起,把相关内容混合排列。概率问题会引起学生学习测度论的兴趣,而测度论知识又反过来应用到概率论中。《概率与测度(第3版)》主要内容包括概率、测度、积分、随机变量及数学期望、分布的收敛的问题、导数与条件期望,随机过程等。
点击链接进入英文版:
Probability and Measure, 3E
概率统计 豆瓣
作者: 德格鲁特 出版社: 人民邮电出版社 2007 - 3
本书内容包括概率论、数理统计两部分,涉及条件概率、随机变量及其分布、数学期望、特殊分布、估计、估计量的抽样分布、假设检验、分类数据与非参数方法、线性统计模型、随机模拟等.本书知识体系结构与国内主流的概率论与数理统计教材基本一致,但内容取材及例题的安排上都比较新颖,尤其是新增加了一些非常实用而且比较先进的模拟方法.书中最后提供了奇数号习题的解答以及索引. 本书作为概率论与数理统计的教材,适合大学本科高年级学生和研究生用作教材或参考书,也可供统计工作人员用作参考书.