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

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非常不错的书，值得购买

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包装满意，交货运输都及时，总体感觉不错！

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商品质量很好，很实用。

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泛函分析是分析数学中最“年轻”的分支，它是古典分析观点的推广，它综合函数论、几何和代数的观点研究无穷维向量空间上的函数、算子、和极限理论。他在二十世纪四十到五十年代就已经成为一门理论完备、内容丰富的数学学科了。

评分☆☆☆☆☆

好书！

评分☆☆☆☆☆

好书，把泛函分析和概率论放在一起，概率论的观点更高了

评分☆☆☆☆☆

商品质量很好，很实用。

评分☆☆☆☆☆

没细看，感觉还可以！

评分☆☆☆☆☆

包装满意，交货运输都及时，总体感觉不错！