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內容簡介

　　《概率論與隨機過程中的泛函分析（影印版）》主要包含國外反映近代數學發展的純數學與應用數學方麵的優秀書籍，天元基金邀請國內各個方嚮的知名數學傢參與選題的工作，經專傢遴選、推薦而齣版。

目錄

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
天元基金影印數學叢書：概率論與隨機過程中的泛函分析（影印版） [Functional Analysis for Probability and Stochastic Processes] 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

內容很全麵，書名包含瞭3門課的名字，內容挺多的，有點難度。

評分☆☆☆☆☆

20世紀初，瑞典數學傢弗列特荷姆和法國數學傢阿達瑪發錶的著作中，齣現瞭把分析學一般化的萌芽。隨後，希爾伯特和海令哲來創瞭“希爾伯特空間”的研究。到瞭二十年代，在數學界已經逐漸形成瞭一般分析學，也就是泛函分析的基本概念。研究無限維綫性空間上的泛函數和算子理論，就産生瞭一門新的分析數學，叫做泛函分析。在二十世紀三十年代，泛函分析就已經成為數學中一門獨立的學科瞭。泛函分析的特點是它不但把古典分析的基本概念和方法一般化瞭，而且還把這些概念和方法幾何化瞭。比如，不同類型的函數可以看作是“函數空間”的點或矢量，這樣最後得到瞭“抽象空間”這個一般的概念。它既包含瞭以前討論過的幾何對象，也包括瞭不同的函數空間。

評分☆☆☆☆☆

《概率論與隨機過程中的泛函分析（影印版）》主要包含國外反映近代數學發展的純數學與應用數學方麵的優秀書籍，天元基金邀請國內各個方嚮的知名數學傢參與選題的工作，經專傢遴選、推薦而齣版。本書包括preliminaries;basic notions;conditional expectation;brownian motion;dual spacess;semigroups of operators and markov processes etc.

評分☆☆☆☆☆

評分☆☆☆☆☆

還不錯，挺好

評分☆☆☆☆☆

不錯，值得看看

評分☆☆☆☆☆

印刷清晰。纔看瞭幾頁，感覺作者挺幽默的，敘述簡潔。

評分☆☆☆☆☆

非常不錯的書，值得購買

評分☆☆☆☆☆

書有點髒，但內容好

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