带跳的随机微分方程理论及其应用（英文版）

图书标准信息

• 作者 司徒荣 著
• 出版社 世界图书出版公司
• 出版时间 2012-01
• 版次 1
• ISBN 9787510040566
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 434页
• 正文语种 简体中文

【内容简介】

《带跳的随机微分方程理论及其应用（英文版）》是一部讲述随机微分方程及其应用的教程。内容全面，讲述如何很好地引入和理解ito积分，确定了ito微分规则，解决了求解sde的方法，阐述了girsanov定理，并且获得了sde的弱解。书中也讲述了如何解决滤波问题、鞅表示定理，解决了金融市场的期权定价问题以及著名的black-scholes公式和其他重要结果。特别地，书中提供了研究市场中金融问题的倒向随机技巧和反射sed技巧，以便更好地研究优化随机样本控制问题。这两个技巧十分高效有力，还可以应用于解决自然和科学中的其他问题。

【目录】

preface
acknowledgement
abbreviationsandsomeexplanations
Ⅰstochasticdifferentialequationswithjumpsinrd
1martingaletheoryandthestochasticintegralforpoint
processes
1.1conceptofamartingale
1.2stoppingtimes.predictableprocess
1.3martingaleswithdiscretetime
1.4uniformintegrabilityandmartingales
1.5martingaleswithcontinuoustime
1.6doob-meyerdecompositiontheorem
1.7poissonrandommeasureanditsexistence
1.8poissonpointprocessanditsexistence
1.9stochasticintegralforpointprocess.squareintegrablemartingales
2brownianmotion,stochasticintegralandito'sformula
2.1brownianmotionanditsnowheredifferentiability
2.2spaces0andz?
2.3ito'sintegralsonl2
2.4ito'sintegralsonl2,loc
2.5stochasticintegralswithrespecttomartingales
2.6ito'sformulaforcontinuoussemi-martingales
2.7ito'sformulaforsemi-martingaleswithjumps
2.8ito'sformulaford-dimensionalsemi-martingales.integrationbyparts
2.9independenceofbmandpoissonpointprocesses
2.10someexamples
2.11strongmarkovpropertyofbmandpoissonpointprocesses
2.12martingalerepresentationtheorem
3stochasticdifferentialequations
3.1strongsolutionstosdewithjumps
3.1.1notation
3.1.2aprioriestimateanduniquenessofsolutions
3.1.3existenceofsolutionsforthelipschitziancase
3.2exponentialsolutionstolinearsdewithjumps
3.3girsanovtransformationandweaksolutionsofsdewithjumps
3.4examplesofweaksolutions
4someusefultoolsinstochasticdifferentialequations
4.1yamada-watanabetypetheorem
4.2tanakatypeformulaandsomeapplications
4.2.1localizationtechnique
4.2.2tanakatypeformulaind-dimensionalspace
4.2.3applicationstopathwiseuniquenessandconvergenceofsolutions
4.2.4tanakatypeformualin1-dimensionalspace
4.2.5tanakatypeformulainthecomponentform
4.2.6pathwiseuniquenessofsolutions
4.3localtimeandoccupationdensityformula
4.4krylovestimation
4.4.1thecasefor1-dimensionalspace
4.4.2thecaseford-dimensionalspace
4.4.3applicationstoconvergenceofsolutionstosdewithjumps
5stochasticdifferentialequationswithnon-lipschitziancoefficients
5.1strongsolutions.continuouscoefficientswithpconditions1
5.2theskorohodweakconvergencetechnique
5.3weaksolutions.continuouscoefficients
5.4existenceofstrongsolutionsandapplicationstoode
5.5weaksolutions.measurablecoefficientcase

Ⅱapplications
6howtousethestochasticcalculustosolvesde
6.1thefoundationofapplications:ito'sformulaandgirsanov'stheorem
6.2moreusefulexamples
7linearandnon-linearfiltering
7.1solutionsofsdewithfunctionalcoefficientsandgirsanovtheorems
7.2martingalerepresentationtheorems（functionalcoefficientcase）
7.3non-linearfilteringequation
7.4optimallinearfiltering
7.5continuouslinearfiltering.kalman-bucyequation
7.6kalman-bucyequationinmulti-dimensionalcase
7.7moregeneralcontinuouslinearfiltering
7.8zakaiequation
7.9examplesonlinearfiltering
8optionpricinginafinancialmarketandbsde
8.1introduction
8.2amoredetailedderivationofthebsdeforoptionpricing
8.3existenceofsolutionswithboundedstoppingtimes
8.3.1thegeneralmodelanditsexplanation
8.3.2aprioriestimateanduniquenessofasolution
8.3.3existenceofsolutionsforthelipschitziancase
8.4explanationofthesolutionofbsdetooptionpricing
8.4.1continuouscase
8.4.2discontinuouscase
8.5black-scholesformulaforoptionpricing.twoapproaches
8.6black-scholesformulaformarketswithjumps
8.7moregeneralwealthprocessesandbsdes
8.8existenceofsolutionsfornon-lipschitziancase
8.9convergenceofsolutions
8.10explanationofsolutionsofbsdestofinancialmarkets
8.11comparisontheoremforbsdewithjumps
8.12explanationofcomparisontheorem.arbitrage-freemarket
8.13solutionsforunbounded（terminal）stoppingtimes
8.14minimalsolutionforbsdewithdiscontinuousdrift
8.15existenceofnon-lipschitzianoptimalcontrol.bsdecase
8.16existenceofdiscontinuousoptimalcontrol.bsdesinrl
8.17applicationtopde.feynman-kacformula
9optimalconsumptionbyh-j-bequationandlagrangemethod
9.1optimalconsumption
9.2optimizationforafinancialmarketwithjumpsbythelagrangemethod
9.2.1introduction
9.2.2models
9.2.3maintheoremandproof
9.2.4applications
9.2.5concludingremarks
10comparisontheoremandstochasticpathwisecontrol'
10.1comparisonforsolutionsofstochasticdifferentialequations
10.1.11-dimensionalspacecase
10.1.2componentcomparisonind-dimensionalspace
10.1.3applicationstoexistenceofstrongsolutions.weakerconditions
10.2weakandpathwiseuniquenessfor1-dimensionalsdewithjumps
10.3strongsolutionsfor1-dimensionalsdewithjumps
10.3.1non-degeneratecase
10.3.2degenerateandpartially-degeneratecase
10.4stochasticpathwisebang-bangcontrolforanon-linearsystem
10.4.1non-degeneratecase
10.4.2partially-degeneratecase
10.5bang-bangcontrolford-dimensionalnon-linearsystems
10.5.1non-degeneratecase
10.5.2partially-degeneratecase
11stochasticpopulationconttrolandreflectingsde
11.1introduction
11.2notation
11.3skorohod'sproblemanditssolutions
11.4momentestimatesanduniquenessofsolutionstorsde
11.5solutionsforrsdewithjumpsandwithcontinuouscoef-ficients
11.6solutionsforrsdewithjumpsandwithdiscontinuousco-etticients
11.7solutionstopopulationsdeandtheirproperties
11.8comparisonofsolutionsandstochasticpopulationcontrol
11.9caculationofsolutionstopopulationrsde
12maximumprincipleforstochasticsystemswithjumps
12.1introduction
12.2basicassumptionandnotation
12.3maximumprincipleandadjointequationasbsdewithjumps
12.4asimpleexample
12.5intuitivethinkingonthemaximumprinciple
12.6somelemmas
12.7proofoftheorem354
aashortreviewonbasicprobabilitytheory
a.1probabilityspace,randomvariableandmathematicalex-pectation
a.2gaussianvectorsandpoissonrandomvariables
a.3conditionalmathematicalexpectationanditsproperties
a.4randomprocessesandthekolmogorovtheorem
bspacedandskorohod'smetric
cmonotoneclasstheorems.convergenceofrandomprocesses41
c.1monotoneclasstheorems
c.2convergenceofrandomvariables
c.3convergenceofrandomprocessesandstochasticintegrals
references
index