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[美] 纽勒特 (Nualart D.) 著 / 世界图书出版公司 / 2013-10 / 平装
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Malliavi随机分析和相关论题(第2版)
Therehavebeentenyearssincethepublicationofthefirsteditionofthisbook.Sincethen,newapplicationsanddevelopmentsoftheMalliavincal-culushaveappeared.Inpreparingthissecondeditionwehavetakenintoaccountsomeofthesenewapplications,andinthisspirit,thebookhastwoadditionalchaptersthatdealwiththefollowingtwotopics:FYactionalBrownianmotionandMathematicalFinance.
Introduction1AnalysisontheWienerspace1.1Wienerchaosandstochasticintegrals1.1.1TheWienerchaosdecomposition1.1.2Thewhitenoisecase:MultipleWiener-Itointegrals1.1.3Itostochasticcalculus1.2Thederivativeoperator1.2.1Thederivativeoperatorinthewhitenoisecase1.3Thedivergenceoperator1.3.1Propertiesofthedivergenceoperator1.3.2TheSkorohodintegral1.3.3TheItostochasticintegralasaparticularcaseoftheSkorohodintegral1.3.4StochasticintegralrepresentationofWienerfunctionals1.3.5Localproperties1.4TheOrnstein-Uhlenbecksemigroup1.4.1ThesemigroupofOrnstein-Uhlenbeck1.4.2ThegeneratoroftheOrnstein-Uhlenbecksemigroup1.4.3Hypercontractivitypropertyandthemultipliertheorem1.5Sobolevspacesandtheequivalenceofnorms2Regularityofprobabilitylaws2.1Regularityofdensitiesandrelatedtopics2.1.1Computationandestimationofprobabilitydensities2.1.2Acriterionforabsolutecontinuitybasedontheintegration-by-partsformula2.1.3AbsolutecontinuityusingBouleauandHirsch'sapproach2.1.4Smoothnessofdensities2.1.5Compositionoftempereddistributionswithnondegeneraterandomvectors2.1.6Propertiesofthesupportofthelaw2.1.7Regularityofthelawofthemaximumofcontinuousprocesses2.2Stochasticdifferentialequations2.2.1Existenceanduniquenessofsolutions2.2.2Weakdifferentiabilityofthesolution2.3HypoellipticityandHormander'stheorem2.3.1AbsolutecontinuityinthecaseofLipschitzcoefficients2.3.2AbsolutecontinuityunderHormander'sconditions2.3.3SmoothnessofthedensityunderHormander'scondition2.4Stochasticpartialdifferentialequations2.4.1Stochasticintegralequationsontheplane2.4.2Absolutecontinuityforsolutionstothestochasticheatequation3Anticipatingstochasticcalculus3.1Approximationofstochasticintegrals3.1.1StochasticintegralsdefinedbyRiemanns3.1.2TheapproachbasedontheL2developmeoftheprocess3.2Stochasticcalculusforanticipatingintegrals3.2.1Skorohodintegralprocesses3.2.2ContinuityandquadraticvariationoftheSkorohodintegral3.2.3Ito'sformulafortheSkorohodandStratonovichintegrals3.2.4Substitutionformulas3.3Anticipatingstochasticdifferentialequations3.3.1StochasticdifferentialequationsintheSratonovichsense3.3.2Stochasticdifferentialequationswithboundaryconditions……4TransformationsoftheWienermeasure5FractionalBrownianmotion6MalliavinCalculusinfinanceAAppendixReferencesIndex
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