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1、SEMI-MARKOVRISKMODELSFORFINANCE,INSURANCEANDRELIABILITYSEMI-MARKOVRISKMODELSFORFINANCE,INSURANCEANDRELIABILITYByJACQUESJANSSENSolvayBusinessSchool,Brussels,BelgiumRAIMONDOMANCAUniversitàdiRoma“LaSapienza,”ItalyLibraryofCongressControlNumber:2006940397ISBN-10:0-387-70729-8e-ISBN:0-387-70730-1ISB
2、N-13:978-0-387-70729-7Printedonacid-freepaper.AMSSubjectClassifications:60K15,60K20,65C50,90B25,91B28,91B30?2007SpringerScience+BusinessMedia,LLCAllrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthepublisher(SpringerScience+BusinessMedia,LLC,233Spri
3、ngStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden.Theuseinthispublicationoftrad
4、enames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.PrintedintheUnitedStatesofAmerica.987654321springer.comContentsPrefaceXV1ProbabilityToolsforStochasticModelling11TheSampleSpace1
5、2ProbabilitySpace23RandomVariables64Integrability,ExpectationandIndependence85MainDistributionProbabilities145.1TheBinomialDistribution155.2ThePoissonDistribution165.3TheNormal(orLaplace-Gauss)Distribution165.4TheLog-NormalDistribution195.5TheNegativeExponentialDistribution205.6TheMultidimensio
6、nalNormalDistribution206Conditioning(FromIndependencetoDependence)226.1Conditioning:IntroductoryCase226.2Conditioning:GeneralCase266.3RegularConditionalProbability307StochasticProcesses348Martingales379BrownianMotion402RenewalTheoryandMarkovChains431PurposeofRenewalTheory432MainDefinitions443Cl
7、assificationofRenewalProcesses454TheRenewalEquation505TheUseofLaplaceTransform555.1TheLaplaceTransform555.2TheLaplace-Stieltjes(L-S)Transform556ApplicationofWald’sIdentity567AsymptoticalBehaviouroftheN(t)-Process578DelayedandStati
