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博布罗斯基 著 / 高等教育出版社 / 2008-03 / 平装
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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)
《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。
Preface1Preliminaries,notationsandconventions1.1Elementsoftopology1.2Measuretheory1.3Functionsofboundedvariation.Riemann-Stieltjesintegral1.4Sequencesofindependentrandomvariables1.5Convexfunctions.HolderandMinkowskiinequalities1.6TheCauchyequation2Basicnotionsinfunctionalanalysis2.1Linearspaces2.2Banachspaces2.3Thespaceofboundedlinearoperators3Conditionalexpectation3.1ProjectionsinHilbertspaces3.2Definitionandexistenceofconditionalexpectation3.3Propertiesandexamples3.4TheRadon-NikodymTheorem3.5Examplesofdiscretemartingales3.6Convergenceofself-adjointoperators3.7...andofmartingales4Brownianmotionandl-Iilbertspaces4.1Gaussianfamilies&thedefinitionofBrownianmotion4.2CompleteorthonormalsequencesinaHilbertspace4.3ConstructionandbasicpropertiesofBrownianmotion4.4Stochasticintegrals5Dualspacesandconvergenceofprobabilitymeasures5.1TheHahn-BanachTheorem5.2FormoflinearfunctionalsinspecificBanachspaces5.3Thedualofanoperator5.4Weakandweak*topologies5.5TheCentralLimitTheorem5.6Weakconvergenceinmetricspaces5.7Compactnesseverywhere5.8Notesonothermodesofconvergence6TheGelfandtransformanditsapplications6.1Banachalgebras6.2TheGelfandtransform6.3ExamplesofGelfandtransform6.4ExamplesofexplicitcalculationsofGelfandtransform6.5DensesubalgebrasofC(S)6.6InvertingtheabstractFouriertransform6.7TheFactorizationTheorem7SemigroupsofoperatorsandLevyprocesses7.1TheBanach-SteinhausTheorem7.2CalculusofBanachspacevaluedfunctions7.3Closedoperators7.4Semigroupsofoperators7.5BrownianmotionandPoissonprocesssemigroups7.6Moreconvolutionsemigroups7.7Thetelegraphprocesssemigroup7.8Convolutionsemigroupsofmeasuresonsemigroups8Markovprocessesandsemigroupsofoperators8.1SemigroupsofoperatorsrelatedtoMarkovprocesses8.2TheHille-YosidaTheorem8.3Generatorsofstochasticprocesses8.4Approximationtheorems9Appendixes9.1Bibliographicalnotes9.2Solutionsandhintstoexercises9.3SomecommonlyusednotationsReferencesIndex
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