巴拿赫空间中的概率论

图书标准信息

• 作者 [法]李多科斯（Ledoux M.） 著
• 出版社 世界图书出版公司
• 出版时间 2012-09
• 版次 1
• ISBN 9787510048050
• 定价 99.00元
• 装帧 平装
• 开本 16开
• 纸张 胶版纸
• 页数 480页
• 正文语种 英语

【内容简介】

　　ThisbooktriestopresentsomeofthemainaspectsofthetheoryofProbabilityinBanachspaces，fromthefoundationsofthetopictothelatestdevelopmentsandcurrentresearchquestions.ThepasttwentyyearssawintenseactivityinthestudyofclassicalProbabilityTheoryoninfinitedimensionalspaces.vectorvaluedrandomvariables，boundednessandcontinuityofran-domprocesses，withafruitfulinteractionwithclassicalBanachspacesandtheirgeometry.Alargecommunityofmathematicians，fromclassicalprobabiliststopureanalystsandfunctionalanalysts，participatedtothiscommonachievement.
　　Therecentuseofisoperimetrictoolsandconcentrationofmeasurephenomena，andofabstractrandomprocesstechniqueshasledtodaytoratheracompletepictureofthefield.Thesedevelopmentspromptedtheauthorstoundertakethewritingofthisexpositionbasedonthismodernpointofview.
　　Thisbookdoesnotpretendtocoveralltheaspectsofthesubjectandofitsconnectionswithotherfields.Inspiteofitsommissions，imperfectionsanderrors，forwhichwewouldliketoapologize，wehopethatthisworkgivesanattractivepictureofthesubjectandwillserveitappropriately.

【目录】

Introduction
Notation
Part0.IsoperimetricBackgroundandGeneralities
Chapter1.IsoperimetricInequalitiesandtheConcentrationofMeasurePhenomenon
1.1omeIsoperimetricInequalitiesontheSphere,inGaussSpaceandontheCube
1.2AnIsoperimetricInequalityforProductMeasures
1.3MartingaleInequalities
NotesandReferences
Chapter2.GeneralitiesonBanachSpaceValuedRandomVariablesandRandomProcesses
2.1BanachSpaceValuedRadonRandomVariables
2.2RandomProcessesandVectorValuedR,a,ndomVariables
2.3SymmetricRandomVariablesandLevy'sInequalities
2.4SomeInequalitiesforRealValuedRandomVariables
NotesandReferences

PartI.BanachSpaceValuedRandomVariablesandTheirStrongLimitingProperties
Chapter3.GaussianRandomVariables
3.1IntegrabilityandTailBehavior
3.2IntegrabilityofGaussianChaos
3.3ComparisonTheorems
NotesandReferences
Chapter4.RademacherAverages
4.1RealRademacherA'verages
4.2TheContractionPrinciple
4,3IntegrabilityandTailBehaviorofRademacherSeries
4.4IntegrabilityofRademacherChaos
4.5ComparisonTheorems
NotesandReferences
Chapter5.StableRandomVariables
5.1R;epresentationofStableRandomVariables
5.2IntegrabilityandTailBehavior
5.3ComparisonTheorems
NotesandReferences
Chapter6.SumsofIndependentRandomVariables
6.1SymmetrizationandSomeInequalitiesforSumsofIndependentRandomVariables
6.2IntegrabilityofSumsofIndependentRandomVariables
6.3ConcentrationandTailBehavior
NotesandR,eferences
Chapter7.TheStrongLawofLargeNumbers
7.1AGeneralStatementforStrongLimitTheorems
7.2ExamplesofLawsofLargeNumbers
NotesandReferences
Chapter8.TheLawofthelteratedLogarithm
8.1Kolmogorov'sLawoftheIteratedLogarithm
8.2Hartman-Wintner-Strassen'sLawoftheIteratedLogarithm
8.3OntheIdentificationoftheLimits
NotesandReferences

PartII.TightnessofVectorValuedR,andomVariablesandRegularityofRandomProcesses
……