天元基金影印数学丛书：概率论与随机过程中的泛函分析（影印版） [Functional Analysis for Probability and Stochastic Processes] pdf epub mobi txt 电子书 下载 2025

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博布罗斯基 著

出版社： 高等教育出版社

ISBN：9787040236064

版次：1

商品编码：10000723

包装：平装

外文名称：Functional Analysis for Probability and Stochastic Processes

开本：32开

出版时间：2008-03-01

页数：303

正文语种：中文

内容简介

　　《概率论与随机过程中的泛函分析（影印版）》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

评分☆☆☆☆☆

合著8种），主编《设计教育研究》丛刊。合著《视觉传达设计原理》获江苏省第十届社会科学优秀成果奖三等奖。作品多幅入选第6、7、8、9、10届全国美展、历届全国水彩粉画展、中国水彩画100年大展等展览，并获第10届全国美展银奖、第5届全国水彩粉画展铜奖，95全国室内评比一等奖等多项奖项。作品公共艺术多件为北京人民大会堂江苏厅、上海金茂大厦等单位采用。2001年江苏省优秀教师等称号，为中国美术家协会会员，中国流行色协会会员，江苏省美术家协会理事，江苏省壁画学会副会长。

评分☆☆☆☆☆

已经看了50页，书中小错误还是较多，不过都比较明显

评分☆☆☆☆☆

看了前几页 应该还可以 对学过泛函分析和测度论的应该很简单

评分☆☆☆☆☆

还不错，挺好

评分☆☆☆☆☆

内容很全面，书名包含了3门课的名字，内容挺多的，有点难度。

评分☆☆☆☆☆

对于概率、统计等专业的学生欲结合本专业背景学习泛函的话，这是很合适的一本。天元基金资助出版，使得本书价格甚至比普通国内教材还低，值得看。

评分☆☆☆☆☆

景

评分☆☆☆☆☆

不错，貌似有点难度 ~~

评分☆☆☆☆☆

包装满意，交货运输都及时，总体感觉不错！