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页数:142页
时间:2019-08-05
《introduction of SP in continuous time》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
1、AnIntroductiontoStochasticProcessesinContinuousTimeFloraSpieksmaadaptationofthetextbyHarryvanZantentobeusedatyourownexpenseJune9,2013Contents1StochasticProcesses11.1Introduction......................................11.2Finite-dimensionaldistributions......................
2、.....61.3Kolmogorov'scontinuitycriterion..........................71.4Gaussianprocesses..................................121.5Non-dierentiabilityoftheBrowniansamplepaths................151.6Filtrationsandstoppingtimes............................171.7Exercises............
3、...........................242Martingales282.1Denitionandexamples...............................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.......................................603MarkovProcesses683.1Basicdenitions:amystication?..........................683.2Existenceofacanonicalversion...........................773.3StrongMarkov
8、property...............................80iiiCONTENTS3.3.1StrongMarkovproperty...................
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