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1、StochasticDifferentialEquations:TheoryandApplicationsLUDWIGARNOLDAWILEY-INTERSCIENCEPUBLICATIONJOHNWILEY&SONS,NewYork0London0SydneyTorontoOriginalGermanlanguageeditionpublishedbyR.OldenbourgVerlag,Munich.Copyright?1973byR.OldenbourgVerlag.Copyright?1974,byJohnWiley&Sons,Inc.Allrightsreserved.Publish
2、edsimultaneouslyinCanada.Nopartofthisbookmaybereproducedbyanymeans,nortransmitted,nortranslatedintoamachinelanguagewith-outthewrittenpermissionofthepublisher.LibraryofCongressCataloginginPublicationData:Arnold,Ludwig,1937-Stochasticdifferentialequations."AWiley-Intersciencepublication."Translationof
3、StochastischeDifferentialgleichengen.Bibliography:p.1.Stochasticdifferentialequations.I.Title.QA274.23.A7713519.273-22256ISBN0-471-03359-6PrintedintheUnitedStatesofAmerica10987654321PreluceThetheoryofstochasticdifferentialequationswasoriginallydevelopedbymathematiciansasatoolforexplicitconstructiono
4、fthetrajectoriesofdiffusionprocessesforgivencoefficientsofdriftanddiffusion.Inthephysicalandengi-neeringsciences,ontheotherhand,stochasticdifferentialequationsariseina,quitenaturalmannerinthedescriptionofsystemsonwhichso-called"whitenoise"acts.Asaresultofthisvarietyinthemotivations,theexistingdetail
5、edstudiesofthesubject,asarule,eitherarenotwrittenfromastandpointofapplicationsorareinaccessibletothepersonintendingtoapplythem.ThisholdsfortheimportantoriginalworkofIto[42]aswellasthebooksbyGikhmanandSkorokhod[5],Dynkin[211,McKean[451,andSkorokhod[471.Theshorteraccountsofsto-chasticdynamicsystemsinb
6、ooksonstability,filtering,andcontrol(see,forexample,BucyandJoseph[611,Khas'minskiy[65],Jazwinski[66],orKushner[72])areratherunsuitedforthestudyandunderstandingofthesubject.Becauseofthelanguagebarrier,thecomprehensivebookbyGikhmanandSkorokhod[36]inRussianislikelytobeinaccessibletomostpersonsintereste
7、dinthesub-ject.(Noteaddedduringprinting:AnEnglishtranslationhasjustbeenpublishedbySpringerVerlag.)Also,toagreatextentitdealswithaconsiderablymoregeneralcase.ThisbookisbasedonacoursethatIgaveinthesumme
