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1、APPLIEDSEMI-MARKOVPROCESSESAPPLIEDSEMI-MARKOVPROCESSESByJACQUESJANSSENSolvayBusinessSchool,Brussels,BelgiumRAIMONDOMANCAUniversitadiRoma"LaSapienza,"ItalySpringerLibraryofCongressControlNumber:2005933791ISBN-10:0-387-29547-Xe-ISBN0-387-29548-8ISBN-13:978-0387-29547-3Printedonacid-freepape
2、r.AMSSubjectClassifications:60K05,60J10,60K15,60K10,60K20,62P05,65C40,65C99,91B30,91B7Q©2006SpringerScience+BusinessMedia,Inc.Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience-t-BusinessMedia,Inc.,233SpringStreet,N
3、ewYork,NY10013,USA),exceptforbriefexcerptsmconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftradename
4、s,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.987654321springeronline.comContentsPreface1Probabilitytoolsforstochasticmodelling11Thesamples
5、pace12Probabilityspace33Randomvariables74Integrability,ExpectationandIndependence105Maindistributionprobabilities165.1Thebinomialdistribution165.2ThePoissondistribution175.3Thenormal(orLaplace-Gauss)distribution185.4Thelog-normaldistribution205.5Thenegativeexponentialdistribution215.6Them
6、ultidimensionalnormaldistribution226Conditioning(Fromindependencetodependence)246.1Conditioning:introductorycase246.2Conditioning:generalcase286.3Regularconditionalprobability327Stochasticprocesses368Martingales409Brownianmotion432Renewaltheory451Purpose452Maindefinitions463Classification
7、ofrenewalprocesses474Therenewalequation525TheuseofLaplacetransform595.1TheLaplacetransform595.2TheLaplace-Stieltjestransform645.3Anapplicationtotherenewalfunction666ApplicationofWald'sidentity676.1Wald'sidentity676.2AlowerboundforrenewalfunctionR687Asymptoticalbehav
