扩散 马尔科夫过程和鞅（第1卷）

图书标准信息

• 作者 L.C.G.Rogers、D.Williams 著
• 出版社 世界图书出版公司
• 出版时间 2003-01
• 版次 1
• ISBN 9787506259217
• 定价 63.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 386页

【内容简介】

　　Longago（orsoitseemstoday），Chungwroteonpage196ofhisbook[1]：Onewondersifthepresenttheoryofstochasticprocessesisnotstilltoodifficultforapplications.Advancesinthetheorysincethattimehavebeenphenomenal，butthesehavebeenaccompaniedbyanincreaseinthetechnicaldifficultyofthesubjectsobewilderingastogiveaquaintcharmtoChungsuseofthewordstill.Meyerwritesintheprefacetohisdefinitiveaccountofstochasticintegraltheory：…ilfaut…uncoursdesixmoissurlesdefinitions.Quepeutonyfaire?
　　IhavethoughtupasintuitiveapictureofthesubjectasIcan，writtenitdownatspeed，andrefusedtobeluredbackbypiety（orevenbywit!）tocancelhalfaline.Firstintuition，whichiswhatyouneedwhenyouarelearningthesubject，israw，roughandready;and，asyouhaveguessed，Imaketheexcusethatitdemandsacompatiblestyleandlackofpolish.
　　NotethatIwrotefirstintuition.Consideranexample.MeyersconceptofarightprocessisexactlyrightforMarkovprocesstheory，buttheconceptistheresultofalongevolution.Tounderstanditproperly，youneedahighlydevelopedintuition，andthattakestimetoacquire.Thedifficultywiththebestadvancedliteratureisthatitsauthorshavetoomuchintuition;nevermakethemistakeofthinkingotherwise.
　　此书为英文版！

【目录】

SomeFrequentlyUsedNotation
CHAPTERⅠ.BROWNIANMOTION
1.INTRODUCTION
1.WhatisBrownianmotion,andwhystudyit
2.Brownianmotionasamartingale
3.BrownianmotionasaGaussianprocess
4.BrownianmotionasaMarkovprocess
5.Brownianmotionasadiffusionandmartingale
2.BASICSABOUTBROWNIANMOTION
6.ExistenceanduniquenessofBrownianmotion
7.Skorokhodembedding
8.DonskersInvariancePrinciple
9.Exponentialmartingalesandfirst-passagedistributions
10.Somesample-pathproperties
11.Quadraticvariation
12.ThestrongMarkovproperty
13.Reflection
14.ReflectingBrownianmotionandlocaltime
15.Kolmogorovstest
16.BrownianexponentialmartingalesandtheLawoftheIteratedLogarithm
3.BROWNIANMOTIONINHIGHERDIMENSIONS
17.SomemartingalesforBrownianmotion
18.Recurrenceandtransienceinhigherdimensions
19.SomeapplicationsofBrownianmotiontocomplexanalysis
20.WindingsofplanarBrownianmotion
21.Multiplepoints,conepoints,cutpoints
22.PotentialtheoryofBrownianmotioninRdd≥3
23.Brownianmotionandphysicaldiffusion
4.GAUSSIANPROCESSESANDLEVYPROCESSES
Gaussianprocesses
24.ExistenceresultsforGaussianprocesses
25.Continuityresults
26.Isotropicrandomflows
27.DynkinsIsomorphismTheorem
Levyprocesses
28.Levyprocesses
29.FluctuationtheoryandWiener-Hopffactorisation
30.LocaltimeofLevyprocesses
CHAPTERⅡ.SOMECLASSICALTHEORY
1.BASICMEASURETHEORY
Measurabilityandmeasure
1.Measurablespaces;a-algebras;n-systems;d-systems
2.Measurablefunctions
3.Monotone-ClassTheorems
4.Measures;theuniquenesslemma;almosteverywhere;a.e.u,∑
5.CaratheodorysExtensionTheorem
6.Innerandouteru-measures;completion
Integration
7.Definitionoftheintegralfdu
8.Convergencetheorems
9.TheRadon-NikodymTheorem;absolutecontinuity;<10.Inequalities;andspacesp≥1
Productstructures
11.Producta-algebras
12.Productmeasure;FubinisTheorem
13.Exercises
2.BASICPROBABILITYTHEORY
Probabilityandexpectation
14.Probabilitytriple;almostsurelya.s.;a.s.P,a.s.P,F
15.limsupEn:FirstBorel-CantelliLemma
16.Lawofrandomvariable;distributionfunction:jointlaw
17.Expectation:EX;F
18.Inequalities:Markov,Jensen,Schwarz,Tchebychev
19.Modesofconvergenceofrandomvariables
UniformintegrabilityandL1convergence
20.Uniformintegrability
21.L1convergence
Independence
22.Independenceofa-algebrasandofrandomvariables
23.Existenceoffamiliesofindependentvariables
24.Exercises
3.STOCHASTICPROCESSES
4.DISCRETE-PARAMETERMARTINGALETHEORY
5.CONTINUOUS-PARAMETERSUPERMARTINGALES
CHAPTERⅢ.MARKOVPROCESSES
1.TRANSITIONFUNCTIONSANDRESOLVENTS
2.FELLER-DYNKINPROCESSES
3.ADDITIVEFUNCTIONALS
4.APPROACHTORAYPROCESSES:
5.RAYPROCESSES
6.APPLICATIONS
ReferencesforVolumes1and2
IndextoVolumes1and2