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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：
31.70 元
版面字数：
450.00千字
开本：
16开
装帧形式：
平装
页数：
408
最新
印次时间：
暂无
ISBN：
978-7-04-023606-4
物料号：
23606-00
出版时间：
2018-11-20
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
  • 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 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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