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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☆☆☆☆☆

不錯，貌似有點難度 ~~

評分☆☆☆☆☆

書有點髒，但內容好

評分☆☆☆☆☆

泛函分析對於研究現代物理學是一個有力的工具。n維空間可以用來描述具有n個自由度的力學係統的運動，實際上需要有新的數學工具來描述具有無窮多自由度的力學係統。比如梁的震動問題就是無窮多自由度力學係統的例子。一般來說，從質點力學過渡到連續介質力學，就要由有窮自由度係統過渡到無窮自由度係統。現代物理學中的量子場理論就屬於無窮自由度係統。

評分☆☆☆☆☆

英文版的書，寫的不錯，推薦

評分☆☆☆☆☆

沒細看，感覺還可以！

評分☆☆☆☆☆

泛函分析對於研究現代物理學是一個有力的工具。n維空間可以用來描述具有n個自由度的力學係統的運動，實際上需要有新的數學工具來描述具有無窮多自由度的力學係統。比如梁的震動問題就是無窮多自由度力學係統的例子。一般來說，從質點力學過渡到連續介質力學，就要由有窮自由度係統過渡到無窮自由度係統。現代物理學中的量子場理論就屬於無窮自由度係統。

評分☆☆☆☆☆

買瞭參考用的，查的時候用一下。

評分☆☆☆☆☆

沒細看，感覺還可以！

評分☆☆☆☆☆

好書，把泛函分析和概率論放在一起，概率論的觀點更高瞭

類似圖書 點擊查看全場最低價