随机过程用的极限定理（第2版）

图书标准信息

• 作者 [法]杰克德（Jean Jacod） 著
• 出版社 世界图书出版公司
• 出版时间 2013-10
• 版次 2
• ISBN 9787510061387
• 定价 89.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 660页
• 正文语种 英语

【内容简介】

　　Apartfromcorrectinganumberofprintingmistakes，andsomemathematicalinaccuraciesaswell，thissecondeditioncontainssomenewmaterial:indeed，duringthefifteenyearselapsedsincethefirsteditioncameout，alargenumberofnewresultsconcerninglimittheoremshaveofcoursebeenprovedbymanyauthors，andmoregenerallymathematicallifehasbeengoingon.Thisgaveusthefeelingthatsomeofthematerialinthefirsteditionwasperhapsnotasimportantaswethoughtatthetime，whilethereweresomeneglectedtopicswhichhaveinfactprovedtobeveryusefulinvariousapplications.
　　Soperhapsatotallynewbookwouldhavebeenagoodthingtowrite.Ournaturallazinesspreventedustodothat，butwehavefeltcompelledtofillinthemostevidentholesinthisbook.Thishasbeendoneinthemostpainlesswayforus，andalsoforthereaderacquaintedwiththefirstedition（atleastwehopeso...）.Thatisallnewmaterialhasbeenaddedattheendofpreexistingchapters.

【目录】

ChapterⅠTheGeneralTheoryofStochasticProcesses,SemimartingalesandStochasticIntegrals
1.StochasticBasis,StoppingTimes,Optionala-Field,Martingales
a.StochasticBasis
b.StoppingTimes
c.TheOptionalσ-Field
d.TheLocalizationProcedure
e.Martingales
f.TheDiscreteCase
2.Predictableσ-Field,PredictableTimes
a.ThePredictableσ-Field
b.PredictableTimes
c.TotallyInaccessibleStoppingTimes
d.PredictableProjection
e.TheDiscreteCase
3.IncreasingProcesses
a.BasicProperties
b.Doob-MeyerDecompositionandCompensatorsofIncreasingProcesses
c.LenglartDominationProperty
d.TheDiscreteCase
4.SemimartingalesandStochasticIntegrals
a.LocallySquare-IntegrableMartingales
b.DecompositionsofaLocalMartingale
c.Semimartingales
d.ConstructionoftheStochasticIntegral
e.QuadraticVariationofaSemimartingaleandIto'sFormula
f.Doleans-DadeExponentialFormula
g.TheDiscreteCase

ChapterⅡCharacteristicsofSemimartingalesandProcesseswithIndependentIncrements
1.RandomMeasures
1a.GeneralRandomMeasures
1b.Integer-ValuedRandomMeasures
1c.AFundamentalExample:PoissonMeasures
1d.StochasticIntegralwithRespecttoaRandomMeasure
2.CharacteristicsofSemimartingales
2a.DefinitionoftheCharacteristics
2b.IntegrabilityandCharacteristics
2c.ACanonicalRepresentationforSemimartingales
2d.CharacteristicsandExponentialFormula
3.SomeExamples
3a.TheDiscreteCase
3b.MoreontheDiscreteCase
3c.The"One-Point"PointProcessandEmpiricalProcesses
4.SemimartingaleswithIndependentIncrements
4a.WienerProcesses
4b.PoissonProcessesandPoissonRandomMeasures
4c.ProcesseswithIndependentIncrementsandSemimartingales
4d.GaussianMartingales
5.ProcesseswithIndependentIncrementsWhichAreNotSemimartingales
5a.TheResults
5b.TheProofs
6.ProcesseswithConditionallyIndependentIncrements
7.ProgressiveConditionalContinuousPIIs
8.Semimartingales,StochasticExponentialandStochasticLogarithm
8a.MoreAboutStochasticExponentialandStochasticLogarithm,
8b.MultiplicativeDecompositionsandExponentiallySpecialSemimartingales
ChapterⅢMartingaleProblemsandChangesofMeasures
1.MartingaleProblemsandPointProcesses
1a.GeneralMartingaleProblems
1b.MartingaleProblemsandRandomMeasures
1c.PointProcessesandMultivariatePointProcesses
……
ChapterⅣBellingerProcesses,AbsoluteContinuity
ChapterⅤContiguity,EntireSeparation,ConvergenceinVariation
ChapterⅥSkorokhodTopologyandConvergenceofProcesses
ChapterⅦConvergenceofProcesseswithIndependentIncrements
ChapterⅧConvergencetoaProcesswithIndependentIncrements
ChapterⅨConvergencetoaSemimartingale
ChapterⅩLimitTheorems,DensityProcessesandContiguityBibliographicalComments
References
IndexofSymbols
IndexofTerminology
IndexofTopics
IndexofConditionsforLimitTheorems