随机偏微分方程基础教程

《随机偏微分方程基础教程》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、AnIntroductiontoStochasticPDEsJuly23,2009MartinHairerTheUniversityofWarwick/CourantInstituteContents1Introduction11.1Acknowledgements......................................22SomeMotivatingExamples22.1Amodelforarandomstring(polymer)............................22.2ThestochasticNavier-St

2、okesequations...........................32.3Thestochasticheatequation.................................42.4Whathavewelearned?....................................63GaussianMeasureTheory73.1A-prioriboundsonGaussianmeasures............................103.2TheCameron-Martinspace..........

3、........................163.3ImagesofGaussianmeasures.................................213.4CylindricalWienerprocessesandstochasticintegration...................244APrimeronSemigroupTheory284.1Stronglycontinuoussemigroups...............................294.2Semigroupswithselfadjointgen

4、erators............................344.3Analyticsemigroups.....................................354.4Interpolationspaces......................................39arXiv:0907.4178v1[math.PR]23Jul20095LinearSPDEs/StochasticConvolutions445.1Timeandspaceregularity............................

5、.......475.2Long-timebehaviour.....................................505.3Convergenceinothertopologies...............................556SemilinearSPDEs636.1Localsolutions........................................636.2InterpolationinequalitiesandSobolevembeddings.....................666.3

6、Reaction-diffusionequations.................................706.4ThestochasticNavier-Stokesequations...........................731IntroductionThesenotesarebasedonaseriesoflecturesgivenfirstattheUniversityofWarwickinspring2008andthenattheCourantInstituteinspring2009.Itisanattempttogive

7、areasonablyself-containedpresentationofthebasictheoryofstochasticpartialdifferentialequations,takingforgrantedbasicmeasuretheory,functionalanalysisandprobabilitytheory,butnothingelse.Sincetheaimwastopresentmostofthematerialcoveredinthesenotesduringa30-hoursseriesofpostgraduatelecture

8、,suchanattem