Malliavi随机分析和相关论题（第2版）

图书标准信息

• 作者 [美]纽勒特（Nualart D.） 著
• 出版社 世界图书出版公司
• 出版时间 2013-10
• 版次 2
• ISBN 9787510061370
• 定价 59.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 382页
• 正文语种 英语

【内容简介】

　　Therehavebeentenyearssincethepublicationofthefirsteditionofthisbook.Sincethen，newapplicationsanddevelopmentsoftheMalliavincal-culushaveappeared.Inpreparingthissecondeditionwehavetakenintoaccountsomeofthesenewapplications，andinthisspirit，thebookhastwoadditionalchaptersthatdealwiththefollowingtwotopics:FYactionalBrownianmotionandMathematicalFinance.

【目录】

Introduction
1AnalysisontheWienerspace
1.1Wienerchaosandstochasticintegrals
1.1.1TheWienerchaosdecomposition
1.1.2Thewhitenoisecase:MultipleWiener-Itointegrals
1.1.3Itostochasticcalculus
1.2Thederivativeoperator
1.2.1Thederivativeoperatorinthewhitenoisecase
1.3Thedivergenceoperator
1.3.1Propertiesofthedivergenceoperator
1.3.2TheSkorohodintegral
1.3.3TheItostochasticintegralasaparticularcaseoftheSkorohodintegral
1.3.4StochasticintegralrepresentationofWienerfunctionals
1.3.5Localproperties
1.4TheOrnstein-Uhlenbecksemigroup
1.4.1ThesemigroupofOrnstein-Uhlenbeck
1.4.2ThegeneratoroftheOrnstein-Uhlenbecksemigroup
1.4.3Hypercontractivitypropertyandthemultipliertheorem
1.5Sobolevspacesandtheequivalenceofnorms

2Regularityofprobabilitylaws
2.1Regularityofdensitiesandrelatedtopics
2.1.1Computationandestimationofprobabilitydensities
2.1.2Acriterionforabsolutecontinuitybasedontheintegration-by-partsformula
2.1.3AbsolutecontinuityusingBouleauandHirsch'sapproach
2.1.4Smoothnessofdensities
2.1.5Compositionoftempereddistributionswithnondegeneraterandomvectors
2.1.6Propertiesofthesupportofthelaw
2.1.7Regularityofthelawofthemaximumofcontinuousprocesses
2.2Stochasticdifferentialequations
2.2.1Existenceanduniquenessofsolutions
2.2.2Weakdifferentiabilityofthesolution
2.3HypoellipticityandHormander'stheorem
2.3.1AbsolutecontinuityinthecaseofLipschitzcoefficients
2.3.2AbsolutecontinuityunderHormander'sconditions
2.3.3SmoothnessofthedensityunderHormander'scondition
2.4Stochasticpartialdifferentialequations
2.4.1Stochasticintegralequationsontheplane
2.4.2Absolutecontinuityforsolutionstothestochasticheatequation

3Anticipatingstochasticcalculus
3.1Approximationofstochasticintegrals
3.1.1StochasticintegralsdefinedbyRiemanns
3.1.2TheapproachbasedontheL2developmeoftheprocess
3.2Stochasticcalculusforanticipatingintegrals
3.2.1Skorohodintegralprocesses
3.2.2ContinuityandquadraticvariationoftheSkorohodintegral
3.2.3Ito'sformulafortheSkorohodandStratonovichintegrals
3.2.4Substitutionformulas
3.3Anticipatingstochasticdifferentialequations
3.3.1StochasticdifferentialequationsintheSratonovichsense
3.3.2Stochasticdifferentialequationswithboundaryconditions
……

4TransformationsoftheWienermeasure
5FractionalBrownianmotion
6MalliavinCalculusinfinance
AAppendix
References
Index