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1、ThispageintentionallyleftblankCAMBRIDGESTUDIESINADVANCEDMATHEMATICS120EditorialBoardB.BOLLOBAS,W.FULTON,A.KATOK,F.KIRWAN,′P.SARNAK,B.SIMON,B.TOTAROMULTIDIMENSIONALSTOCHASTICPROCESSESASROUGHPATHSRoughpathanalysisprovidesafreshperspectiveonIto’simportanttheoryof?stoch
2、asticdifferentialequations.Keytheoremsofmodernstochasticanalysis(existenceandlimittheoremsforstochastic?ows,Freidlin–Wentzelltheory,theStroock–Varadhansupportdescription)canbeobtainedwithdramaticsimpli?cations.Classicalapproximationresultsandtheirlimitations(Wong–Za
3、kai,McShane’scounterexample)receive“obvious”roughpathexplanations.Evidenceisbuildingthatroughpathswillplayanimportantroleinthefutureanalysisofstochasticpartialdifferentialequations,andtheauthorsincludesome?rstresultsinthisdirection.Theyalsoemphasizeinteractionswitho
4、therpartsofmathematics,includingCaratheodorygeometry,DirichletformsandMalliavincalculus.Basedonsuccessfulcoursesatthegraduatelevel,thisup-to-dateintroductionpresentsthetheoryofroughpathsanditsapplicationstostochasticanalysis.Examples,explanationsandexercisesmaketheb
5、ookaccessibletograduatestudentsandresearchersfromavarietyof?elds.CAMBRIDGESTUDIESINADVANCEDMATHEMATICSEditorialBoard:B.Bollobas,W.Fulton,A.Katok,F.Kirwan,P.Sarnak,B.Simon,B.Totaro′AllthetitleslistedbelowcanbeobtainedfromgoodbooksellersorfromCambridgeUniversityPress.
6、Foracompleteserieslistingvisit:http://www.cambridge.org/series/sSeries.asp?code=CSAMAlreadypublished70R.Iorio&V.IorioFourieranalysisandpartialdifferentialequations71R.BleiAnalysisinintegerandfractionaldimensions72F.Borceux&G.JanelidzeGaloistheories73B.Bollobas′Rando
7、mgraphs(2ndEdition)74R.M.DudleyRealanalysisandprobability(2ndEdition)75T.Sheil-SmallComplexpolynomials76C.VoisinHodgetheoryandcomplexalgebraicgeometry,I77C.VoisinHodgetheoryandcomplexalgebraicgeometry,II78V.PaulsenCompletelyboundedmapsandoperatoralgebras79F.Gesztesy
8、&H.HoldenSolitonequationsandtheiralgebro-geometricsolutions,I81S.MukaiAnintroductiontoinvariantsandmoduli82G.TourlakisLecturesinlogicandse
