multidimensional stochastic processes as rough paths theory and applications(friz)

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1、ThispageintentionallyleftblankCAMBRIDGESTUDIESINADVANCEDMATHEMATICS120EditorialBoardB.BOLLOBAS,W.FULTON,A.KATOK,F.KIRWAN,´P.SARNAK,B.SIMON,B.TOTAROMULTIDIMENSIONALSTOCHASTICPROCESSESASROUGHPATHSRoughpathanalysisprovidesafreshperspectiveonIto’simportanttheoryofˆstoch

2、asticdifferentialequations.Keytheoremsofmodernstochasticanalysis(existenceandlimittheoremsforstochasticflows,Freidlin–Wentzelltheory,theStroock–Varadhansupportdescription)canbeobtainedwithdramaticsimplifications.Classicalapproximationresultsandtheirlimitations(Wong–Za

3、kai,McShane’scounterexample)receive“obvious”roughpathexplanations.Evidenceisbuildingthatroughpathswillplayanimportantroleinthefutureanalysisofstochasticpartialdifferentialequations,andtheauthorsincludesomefirstresultsinthisdirection.Theyalsoemphasizeinteractionswitho

4、therpartsofmathematics,includingCaratheodorygeometry,DirichletformsandMalliavincalculus.Basedonsuccessfulcoursesatthegraduatelevel,thisup-to-dateintroductionpresentsthetheoryofroughpathsanditsapplicationstostochasticanalysis.Examples,explanationsandexercisesmaketheb

5、ookaccessibletograduatestudentsandresearchersfromavarietyoffields.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