机读格式显示(MARC)
- 000 03812oam2 2200277 450
- 010 __ |a 978-7-04-023606-4 |b |d CNY 31.70
- 100 __ |a 20080508d2008 em y0chiy50 ea
- 200 1_ |a 概率论与随机过程中的泛函分析 |A gai lu lun yu sui ji guo cheng zhong de fan han fen xi |f (英)博布罗斯基
- 210 __ |a 北京 |c 高等教育出版社 |d 2008.03
- 225 2_ |a 天元基金影印数学丛书 |A Tian Yuan Ji Jin Ying Yin Shu Xue Cong Shu
- 327 0_ |a Preface |a 1 Preliminaries, notations and conventions |a 1.1 Elements of topology |a 1.2 Measure theory |a 1.3 Functions of bounded variation. Riemann-Stieltjes integral |a 1.4 Sequences of independent random variables |a 1.5 Convex functions. Holder and Minkowski inequalities |a 1.6 The Cauchy equation |a 2 Basic notions in functional analysis |a 2.1 Linear spaces |a 2.2 Banach spaces |a 2.3 The space of bounded linear operators |a 3 Conditional expectation |a 3.1 Projections in Hilbert spaces |a 3.2 Definition and existence of conditional expectation |a 3.3 Properties and examples |a 3.4 The Radon-Nikodym Theorem |a 3.5 Examples of discrete martingales |a 3.6 Convergence of self-adjoint operators |a 3.7 ... and of martingales |a 4 Brownian motion and l-Iilbert spaces |a 4.1 Gaussian families & the definition of Brownian motion |a 4.2 Complete orthonormal sequences in a Hilbert space |a 4.3 Construction and basic properties of Brownian motion |a 4.4 Stochastic integrals |a 5 Dual spaces and convergence of probability measures |a 5.1 The Hahn-Banach Theorem |a 5.2 Form of linear functionals in specific Banach spaces |a 5.3 Thedual of an operator |a 5.4 Weak and weak* topologies |a 5.5 The Central Limit Theorem |a 5.6 Weak convergence in metric spaces |a 5.7 Compactness everywhere |a 5.8 Notes on other modes of convergence |a 6 The Gelfand transform and its applications |a 6.1 Banach algebras |a 6.2 The Gelfand transform |a 6.3 Examples of Gelfand transform |a 6.4 Examples of explicit calculations of Gelfand transform |a 6.5 Dense subalgebras of C(S) |a 6.6 Inverting the abstract Fourier transform |a 6.7 The Factorization Theorem |a 7 Semigroups of operators and Levy processes |a 7.1 The Banach-Steinhaus Theorem |a 7.2 Calculus of Banach space valued functions |a 7.3 Closed operators |a 7.4 Semigroups of operators |a 7.5 Brownian motion and Poisson process semigroups |a 7.6 More convolution semigroups |a 7.7 The telegraph process semigroup |a 7.8 Convolution semigroups of measures on semigroups |a 8 Markov processes and semigroups of operators |a 8.1 Semigroups of operators related to Markov processes |a 8.2 The Hille-Yosida Theorem |a 8.3 Generators of stochastic processes |a 8.4 Approximation theorems |a 9 Appendixes |a 9.1 Bibliographical notes |a 9.2 Solutions and hints to exercises |a 9.3 Some commonly used notations |a References |a Index
- 330 __ |a 本书是作者在Rice大学和Houston大学给研究生授课的讲义基础上写成的。本书在介绍了泛函分析的基本概念(如Banach空间)后，用Hibert空间泛函的F.Riesz表示定理建立Radon-Nikodym定理，从而引进条件期望的概念；在Hilbert空间的正交分解概念的基础上，引进了Brown运动，并建立了随机积分的概念；证明了Hahn-Banach定理并引进了对偶空间的概念后，便可讨论概率分布的弱收敛及弱拓扑的紧性；在介绍了交换Banach代数的Gelfand表示后，讨论了抽象Fourier变换的反演公式。本书最后两章讨论了算子半群和Levy过程。证明了算子半群的Hille-Yosida定理，讨论了Markov过程与算子半群生成子的关系。 本书可作为高等学校本科高年级和研究生课程教材，对于专攻概率论与泛函分析的读者具有很好的参考价值，也可作为学习概率论和随机过程专著的导引。
- 461 _0 |1 2001 |a 天元基金影印数学丛书
- 606 0_ |a 概率论 |A Gai Lv Lun
- 701 _0 |a 博布罗斯基 |A bo bu luo si ji
- 801 _0 |a CN |b 91MARC |c 20130904
- 905 __ |a LIB |d O211/122