图书信息
图书目录
概率论与随机过程中的泛函分析（影印版）
暂无简介
作者：
Adam Bobrowski
定价：
48.00元
出版时间：
2008-03-28
ISBN：
978-7-04-023606-4
物料号：
23606-00
读者对象：
高等教育
一级分类：
数学与统计学类
二级分类：
数学与应用数学专业课
三级分类：
其他课程
重点项目：
暂无
版面字数：
450.000千字
开本：
16开
全书页数：
393页
装帧形式：
平装
- 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 Hilbert 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 The dual 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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