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概率论与随机过程中的泛函分析（影印版）

作者：
Adam Bobrowski
定价：
48.00元
ISBN：
978-7-04-023606-4
版面字数：
450.000千字
开本：
16开
全书页数：
393页
装帧形式：
平装
重点项目：
暂无
出版时间：
2008-03-28
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
暂无
  • 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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