经典数学教材（影印版）：马尔科夫过程、布朗运动和时间对称（第2版）

图书标准信息

• 作者 [美]钟开来 著
• 出版社 世界图书出版公司
• 出版时间 2013-10
• 版次 2
• ISBN 9787510061462
• 定价 69.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 431页
• 正文语种 英语

【内容简介】

　　Thisbookconsistsoftwoparts，tobecalledPartIandPartn.PartI，Chapterslthrough5，isessentiallyaneweditionofKaiLaiChung'sLec-turesfromMarkovProcessestoBrownianMotion（1982）.Hehascorrectedanumberofmisprintsintheoriginaledition，andhasinsertedafewreferencesandremarks，ofwhichhesays，"Thelattermustberegardedasrandomlyselectedsincetwenty-someyearsisalongtimetoretracesteps..."ThispartintroducesstrongMarkovprocessesandtheirpotentialtheory.Inparticular，itstudiesBrownianmotion，andshowshowitgeneratesclassicalpotentialtheory.

【目录】

Chapter1MarkovPtocess
1.1.MarkovProperty
1.2.TransitionFunction
1.3.OptionalTimes
1.4.MartingaleTheorems
1.5.ProgressiveMeasurabilityandtheSectionTheorem
Exercises
NotesonChapterI

Chapter2BasicProperties
2.1.MartingaleConnection
2.2.FellerProcess
Exercises
2.3.StrongMarkovPropertyandRightContinuityofFields
Exercises
2.4.ModerateMarkovPropertyandQuasiLeftContinuity
Exercises
NotesonChapter2

Chapter3HuntProcess
3.1.DefiningProperties
Exercises
3.2.AnalysisofExcessiveFunctions
Exercises
3.3.HittingTimes
3.4.BalayageandFundamentalStructure
Exercises
3.5.FineProperties
Exercises
3.6.DecreasingLimits
Exercises
3.7.RecurrenceandTransience
Exercises
3.8.Hypothesis(B)
Exerases
NotesonChapter3

Chapter4BrownianMotion
4.1.SpatialHomogeneity
Exercises
4.2.PreliminaryPropertiesofBrownianMotion
Exercises
4.3.HarmonicFunction
Exerases
4.4.DirichletProblem
Exercises
4.5.SuperharmonicFunctionandSupermartingale
Exerases
4.6.TheRoleoftheLaplacian
Exercises
4.7.TheFeynman-KacFunctionalandtheSchrodingerEquation
Exe工ases
NotesonChapter4

Chapter5PotentialDevelopments
5.1QuittingTimeandEquilibriumMeasure
Exercises
5.2.SomePrinciplesofPotentialTheory
Exerases
NotesonChapter5

Chapter6Generalities
6.1EssentialLimits
6.2PenetrationTimes
6.3GeneralTheory
Exercises
NotesonChapter6

Chapter7MarkovChains:aFiresideChat
7.1BasicExamples
NotesonChapter7

Chapter8RayProcesses
8.1RayResolventsandSemigroups
8.2BranchingPoints
Chapter9
ApplicationtoMarkovChains
……
Chapter10TimeReversal
Chapter11h-Transforms
Chapter12DeathandTransfiguration:AFiresideChat
Chapter13ProcessesinDuality
Chapter14TheMartinBoundary
Chapter15TheBasisofDuality:AFiresideChat
Bibliography
Index