连续鞅和布朗运动

图书标准信息

• 作者 瑞韦兹（Revuz.D） 著
• 出版社 世界图书出版公司
• 出版时间 2008-03
• 版次 1
• ISBN 9787506291934
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 606页
• 正文语种 英语

【内容简介】

　　《连续鞅和布朗运动》是一部很经典的讲述随机过程及布朗运动的教材（全英文版）。其旨在尽可能详细的向概率专家介绍尽可能多的有关布朗运动的观点、技巧和方法。自从1991年这《连续鞅和布朗运动》的第一版本问世以来，有关布朗运动和相关的随机过程一直是人们研究和讨论的热点。布朗运动是许多典型的概率问题连续鞅、高斯过程、马尔科夫过程甚至更特殊的具有独立增量的过程的交叉点。大量新的方法都能够成功的应用于它的研究，新的版本也就应运而生。《连续鞅和布朗运动》在第一章引入布朗运动后，以后的各章都是具体在讲述某一种特定的方法或者观点。在这些方法中贯穿于《连续鞅和布朗运动》始终的是随机积分以及强有力的游程理论。

【目录】

Chapter0.Preliminaries
§1.BasicNotation
§2.MonotoneClassTheorem
§3.Completion
§4.FunctionsofFiniteVariationandStieltjesIntegrals
§5.WeakConvergenceinMetricSpaces
§6.GaussianandOtherRandomVariables

ChapterⅠ.Introduction
§1.ExamplesofStochasticProcesses.BrownianMotion
§2.LocalPropertiesofBrownianPaths
§3.CanonicalProcessesandGaussianProcesses
§4.FiltrationsandStoppingTimes
NotesandComments

ChapterⅡ.Martingales
§1.Definitions，MaximalInequalitiesandApplications
§2.ConvergenceandRegularizationTheorems
§3.OptionalStoppingTheorem
NotesandComments

ChapterⅢ.MarkovProcesses
§1.BasicDefinitions
§2.FellerProcesses
§3.StrongMarkovProperty
§4.SummaryofResultsonLevyProcesses
NotesandComments

ChapterⅣ.StochasticIntegration
§1.QuadraticVariations
§2.StochasticIntegrals
§3.ItosFormulaandFirstApplications
§4.Burkholder-Davis-GundyInequalities
§5.PredictableProcesses
NotesandComments

ChapterⅤ.RepresentationofMartingales
§1.ContinuousMartingalesasTime-changedBrownianMotions
§2.ConformalMartingalesandPlanarBrownianMotion
§3.BrownianMartingales
§4.IntegralRepresentations
NotesandComments

ChapterⅥ.LocalTimes
§1.DefinitionandFirstProperties
§2.TheLocalTimeofBrownianMotion
§3.TheThree-DimensionalBesselProcess
§4.FirstOrderCalculus
§5.TheSkorokhodStoppingProblem
NotesandComments

ChapterⅦ.GeneratorsandTimeReversal
§1.InfinitesimalGenerators.
§2.DiffusionsandItoProcesses
§3.LinearContinuousMarkovProcesses
§4.TimeReversalandApplications
NotesandComments

ChapterⅧ.GirsanovsTheoremandFirstApplications
§1.GirsanovsTheorem
§2.ApplicationofGirsanovsTheoremtotheStudyofWienersSpace
§3.FunctionalsandTransformationsofDiffusionProcesses
NotesandComments

ChapterⅨ.StochasticDifferentialEquations
§1.FormalDefinitionsandUniqueness
§2.ExistenceandUniquenessintheCaseofLipschitzCoefficients
§3.TheCaseofHolderCoefficientsinDimensionOne
NotesandComments

ChapterⅩ.AdditiveFunctionalsofBrownianMotion
§1.GeneralDefinitions
§2.RepresentationTheoremforAdditiveFunctionalsofLinearBrownianMotion
§3.ErgodicTheoremsforAdditiveFunctionals
§4.AsymptoticResultsforthePlanarBrownianMotion
NotesandComments

ChapterⅪ.BesselProcessesandRay-KnightTheorems
§1.BesselProcesses
§2.Ray-KnightTheorems
§3.BesselBridges
NotesandComments

ChapterⅫ.Excursions
§1.PrerequisitesonPoissonPointProcesses
§2.TheExcursionProcessofBrownianMotion
§3.ExcursionsStraddlingaGivenTime
§4.DescriptionsofItosMeasureandApplications
NotesandComments

ChapterXIII.LimitTheoremsinDistribution
§1.ConvergenceinDistribution
§2.AsymptoticBehaviorofAdditiveFunctionalsofBrownianMotion
§3.AsymptoticPropertiesofPlanarBrownianMotion

NotesandComments
Appendix
§1.GronwallsLemma
§2.Distributions
§3.ConvexFunctions
§4.HausdorffMeasuresandDimension
§5.ErgodicTheory
§6.ProbabilitiesonFunctionSpaces
§7.BesselFunctions
§8.Sturm-LiouvilleEquation

Bibliography
IndexofNotation
IndexofTerms
Catalogue