foundations of modern probability - olav kallenberg

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1、FoundationsofModernProbabilityOlavKallenbergSpringerPrefaceSomethirtyyearsagoitwasstillpossible,asLo`evesoablydemonstrated,towriteasinglebookinprobabilitytheorycontainingpracticallyeverythingworthknowinginthesubject.Thesubsequentdevelopmenthasbeenex-plosive,andtodayacorrespondingcomprehensivecovera

2、gewouldrequireawholelibrary.Researchersandgraduatestudentsalikeseemcompelledtoaratherextremedegreeofspecialization.Asaresult,thesubjectisthreatenedbydisintegrationintodozensorhundredsofsubfields.Atthesametimetheinteractionbetweentheareasislivelierthanever,andthereisasteadilygrowingcoreofkeyresultsan

3、dtechniquesthateveryprobabilistneedstoknow,ifonlytoreadtheliteratureinhisorherownfield.Thus,itseemsessentialthatweallhaveatleastageneraloverviewofthewholearea,andweshoulddowhatwecantokeepthesubjecttogether.Thepresentvolumeisanearnestattemptinthatdirection.Myoriginalaimwastowriteabookabout“everything

4、.”Variousspaceandtimeconstraintsforcedmetoacceptmoremodestandrealisticgoalsfortheproject.Thus,“foundations”hadtobeunderstoodinthenarrowersenseoftheearly1970s,andtherewasnoroomforsomeofthemorerecentdevelopments.Iespeciallyregrettheomissionoftopicssuchaslargede-viations,GibbsandPalmmeasures,interacti

5、ngparticlesystems,stochasticdifferentialgeometry,Malliavincalculus,SPDEs,measure-valueddiffusions,andbranchingandsuperprocesses.Clearlyplentyoffundamentalandin-triguingmaterialremainsforapossiblesecondvolume.Evenwithmymorelimited,revisedambitions,Ihadtobeextremelyselectiveinthechoiceofmaterial.Moreim

6、portantly,itwasnecessarytolookforthemosteconomicalapproachtoeveryresultIdiddecidetoinclude.Inthelatterrespect,Iwassurprisedtoseehowmuchcouldactuallybedonetosimplifyandstreamlineproofs,oftenhandeddownthroughgenerationsoftextbookwriters.Mygeneralpreferencehasbeenforresultsconveyingsomenewideaorrelati

7、onship,whereasmanypropositionsofamoretechnicalnaturehavebeenomitted.Inthesamevein,Ihaveavoidedtechnicalorcomputationalproofsthatgivelittleinsightintotheprovenresults.Thisconformswithmyconvictionthatthelogic