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）

图书标准信息

• 作者 博布罗斯基 著
• 出版社 高等教育出版社
• 出版时间 2008-03
• 版次 1
• ISBN 9787040236064
• 定价 31.70元
• 装帧 平装
• 开本 32开
• 纸张 其他
• 页数 303页
• 正文语种 简体中文

【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
1Preliminaries,notationsandconventions
1.1Elementsoftopology
1.2Measuretheory
1.3Functionsofboundedvariation.Riemann-Stieltjesintegral
1.4Sequencesofindependentrandomvariables
1.5Convexfunctions.HolderandMinkowskiinequalities
1.6TheCauchyequation

2Basicnotionsinfunctionalanalysis
2.1Linearspaces
2.2Banachspaces
2.3Thespaceofboundedlinearoperators

3Conditionalexpectation
3.1ProjectionsinHilbertspaces
3.2Definitionandexistenceofconditionalexpectation
3.3Propertiesandexamples
3.4TheRadon-NikodymTheorem
3.5Examplesofdiscretemartingales
3.6Convergenceofself-adjointoperators
3.7...andofmartingales

4Brownianmotionandl-Iilbertspaces
4.1Gaussianfamilies&thedefinitionofBrownianmotion
4.2CompleteorthonormalsequencesinaHilbertspace
4.3ConstructionandbasicpropertiesofBrownianmotion
4.4Stochasticintegrals

5Dualspacesandconvergenceofprobabilitymeasures
5.1TheHahn-BanachTheorem
5.2FormoflinearfunctionalsinspecificBanachspaces
5.3Thedualofanoperator
5.4Weakandweak*topologies
5.5TheCentralLimitTheorem
5.6Weakconvergenceinmetricspaces
5.7Compactnesseverywhere
5.8Notesonothermodesofconvergence

6TheGelfandtransformanditsapplications
6.1Banachalgebras
6.2TheGelfandtransform
6.3ExamplesofGelfandtransform
6.4ExamplesofexplicitcalculationsofGelfandtransform
6.5DensesubalgebrasofC(S)
6.6InvertingtheabstractFouriertransform
6.7TheFactorizationTheorem

7SemigroupsofoperatorsandLevyprocesses
7.1TheBanach-SteinhausTheorem
7.2CalculusofBanachspacevaluedfunctions
7.3Closedoperators
7.4Semigroupsofoperators
7.5BrownianmotionandPoissonprocesssemigroups
7.6Moreconvolutionsemigroups
7.7Thetelegraphprocesssemigroup
7.8Convolutionsemigroupsofmeasuresonsemigroups

8Markovprocessesandsemigroupsofoperators
8.1SemigroupsofoperatorsrelatedtoMarkovprocesses
8.2TheHille-YosidaTheorem
8.3Generatorsofstochasticprocesses
8.4Approximationtheorems

9Appendixes
9.1Bibliographicalnotes
9.2Solutionsandhintstoexercises
9.3Somecommonlyusednotations
References
Index