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1、StochasticPartialDi erentialEquations:AnalysisandNumericalApproximationsArnulfJentzenMay23,20162PrefaceTheselecturenoteshavebeenwrittenforthecourse401-4606-00LNumericalAnal-ysisofStochasticPartialDi erentialEquations"inthespringsemester2014andinthespringsemester2015.Theselecturenotesa
2、refarawayfrombeingcompleteandremainunderconstruction.Inparticular,theselecturenotesdonotyetcontainasuitablecomparisonofthepresentedmaterialwithexistingresults,argumentsandnotionsintheliterature.Thiswillbethesubjectofafutureversionoftheselecturenotes.Furthermore,theselecturenotesdonotco
3、ntainanumberofproofs,argu-mentsandintuitions.Formostofthisadditionalmaterial,thereaderisreferredtothelecturesofthecourse401-4606-00LNumericalAnalysisofStochasticPartialDi erentialEquations"inthespringsemester2014.SonjaCoxandRyanKurniawanaregratefullyacknowledgedfortheirveryhelpfuladvi
4、ceandassistance,especiallyfortheirhelpwiththeMatlabprograms.DanielConusisalsogratefullyacknowl-edgedforseveralcommentsthathelpedtoimprovethepresentationoftheresults.Inaddition,wethankAnttiKnowlesandBennoKuckuckforfruitfuldiscussions.Thestudentsofthecourse401-4606-00LNumericalAnalysiso
5、fStochasticPartialDi erentialEquations"inthespringsemester2014aregratefullyacknowledgedforpointingoutanumberofmisprintstome.SpecialthanksareduetoTimoWeltiforbringinganumberofmisprintstomynotice.Z?urich,March2016ArnulfJentzen3ExercisesSolutionstotheexercisescanbeturnedinthedesignatedmai
6、lboxintheanteroomHGG53.x.Exerc.ExercisesDeadlinesheet1Exerc.1.1.8,1.1.9,1.1.10,&2.2.6.17.03.2016,10:15AM2Exerc.2.3.7,2.4.20,2.4.23,3.4.23,3.6.4,3.6.5,&3.6.18.07.04.2016,10:15AM3Exerc.3.6.26,4.3.3,4.8.7,&6.1.2021.04.2016,10:15AM4Exerc.6.3.1728.04.2016,10:15AM5Exerc.7.1.17&7.1.1812.05.20
7、16,10:15AM6Exerc.7.2.419.05.2016,10:15AM7Exerc.8.1.6&8.1.1426.05.2016,10:15AM8Exerc.8.2.301.06.2016,10:15AM4ContentsIFoundationsinmathematicalanalysis131Gronwall-typeinequalities151.1Propertiesofthebetaandthegammafunction............151.1.1Functionalequationofthegammafunction........
