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1、LectureNotesinMathematicsEditedbyA.DoldandB.Eckmann440RonaldK.GetoorMarkovProcesses:RayProcessesandRightProcessesIIIIIISpringer-VerlagBerlin-HeidelbergNewYork1975Prof.RonaldK.GetoorDepartmentofMathematicsUniversityofCaliforniaSanDiegoP.O.Box109LaJolla,CA92037/USALibraryofCongressCataloginginPu
2、blicationDataOetoor,RonaldKay~1929-Markovprocesses~rayprocessesandrightprocesses.(Lecturenotesinmathematics:440)Bibliography:p.Includesindexes.i.Markovprocesses.I.Title.II.Series:Lecturenotesinmathematics(Berlin);440.qA3.L28no.440[QA274.7]510~.8s[519.2'33i75~6610AMSSubjectClassifications(1970)
3、:60JXX,60J25,60J40,60J45,60J50ISBN3-540-07140-7Springer-VerlagBerlinHeidelberg-NewYorkISBN0-387-07140-7Springer-VerlagNewYorkHeidelbergBerlinThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallythoseoftranslation,reprinting,re-useofillustr
4、ations,broadcasting,reproductionbyphoto-copyingmachineorsimilarmeans,andstorageindatabanks.Under§54oftheGermanCopyrightLawwherecopiesaremadeforotherthanprivateuse,afeeispayabletothepublisher,theamountofthefeetobedeterminedbyagreementwiththepublisher.?bySpringer-VerlagBerlinHeidelberg1975.Print
5、edinGermany.Offsetdruck:JuliusBeltz,Hemsbach/Bergstr.PREFACEThepurposeoftheselecturesistodevelopthebasicpropertiesofRayprocessesandtheirapplicationstoprocessessatisfyingthe"hypothesesdroites"ofMeyerfollowingthefundamentalpaper[16]byMeyerandWalsh.Sections2through7oftheselecturesdiscussthebasicr
6、esultsonRayprocessesand,inoutline,followquitecloselythepresentationinSectioniof[16].However,wegointomoredetailthanin[16]and,inparticular,wegivecompleteproofsofthefactsneededaboutresolventsandsemigroupsinSectionsZand3.BeginninginSection9wegivethebasicapplicationsofRayprocessesto"rightprocesses"
7、againfollowing[16]inoutline.However,wedepartfromMeyerandWalshintwoimportantmatters.Firstlyweassumeonlythatthestatespace~isaU-space,thatis,auniversallymeasurablesubspaceofacompactmetricspace;whereasMeyerandWalshassumethatEisLusinien,that
