天元基金影印数学丛书：概率论与随机过程中的泛函分析（影印版） [Functional Analysis for Probability and Stochastic Processes] 下载 mobi epub pdf 电子书 2025

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内容简介

　　《概率论与随机过程中的泛函分析（影印版）》主要包含国外反映近代数学发展的纯数学与应用数学方面的优秀书籍，天元基金邀请国内各个方向的知名数学家参与选题的工作，经专家遴选、推荐而出版。

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 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
天元基金影印数学丛书：概率论与随机过程中的泛函分析（影印版） [Functional Analysis for Probability and Stochastic Processes] 下载 mobi epub pdf txt 电子书 格式

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合著8种），主编《设计教育研究》丛刊。合著《视觉传达设计原理》获江苏省第十届社会科学优秀成果奖三等奖。作品多幅入选第6、7、8、9、10届全国美展、历届全国水彩粉画展、中国水彩画100年大展等展览，并获第10届全国美展银奖、第5届全国水彩粉画展铜奖，95全国室内评比一等奖等多项奖项。作品公共艺术多件为北京人民大会堂江苏厅、上海金茂大厦等单位采用。2001年江苏省优秀教师等称号，为中国美术家协会会员，中国流行色协会会员，江苏省美术家协会理事，江苏省壁画学会副会长。

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从数学的角度，阐述了概率论和随机过程的泛函分析方法，思路清晰，知识丰富。对理论推演的要求较高。

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内容不错，绝对的好书，而且满减下来很满意哦~一如既往的支持京东！

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终于买到手了，正版很正版，

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joli

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好书好书好书好书好书好书好书好书

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已经看了50页，书中小错误还是较多，不过都比较明显

评分☆☆☆☆☆

已经看了50页，书中小错误还是较多，不过都比较明显

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好书好书好书好书好书好书好书好书

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