introduction of SP in continuous time

introduction of SP in continuous time

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時間：2019-08-05

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1、AnIntroductiontoStochasticProcessesinContinuousTimeFloraSpieksmaadaptationofthetextbyHarryvanZantentobeusedatyourownexpenseJune9,2013Contents1StochasticProcesses11.1Introduction......................................11.2Finite-dimensionaldistributions......................

2、.....61.3Kolmogorov'scontinuitycriterion..........................71.4Gaussianprocesses..................................121.5Non-di erentiabilityoftheBrowniansamplepaths................151.6Filtrationsandstoppingtimes............................171.7Exercises............

3、...........................242Martingales282.1De nitionandexamples...............................282.2Discrete-timemartingales..............................292.2.1Martingaletransforms............................292.2.2Inequalities..................................322.2.3D

4、oobdecomposition.............................342.2.4Convergencetheorems............................352.2.5Optionalsamplingtheorems.........................402.2.6LawofLargenumbers............................412.3Continuous-timemartingales............................422.3.

5、1Upcrossingsincontinuoustime.......................422.3.2Regularisation................................432.3.3Convergencetheorems............................472.3.4Inequalities..................................482.3.5Optionalsampling..............................482.4App

6、licationstoBrownianmotion..........................512.4.1Quadraticvariation.............................512.4.2Exponentialinequality............................522.4.3Thelawoftheiteratedlogarithm......................532.4.4Distributionofhittingtimes.....................

7、....562.5PoissonprocessandthePASTAproperty.....................572.6Exercises.......................................603MarkovProcesses683.1Basicde nitions:amysti cation?..........................683.2Existenceofacanonicalversion...........................773.3StrongMarkov

8、property...............................80iiiCONTENTS3.3.1StrongMarkovproperty...................

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