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1、TheTwo-DimensionalPoissonProcessandExtremalProcessesAuthor(s):JamesPickandsIIISource:JournalofAppliedProbability,Vol.8,No.4(Dec.,1971),pp.745-756Publishedby:AppliedProbabilityTrustStableURL:http://www.jstor.org/stable/3212238.Accessed:08/11/201306:01YouruseoftheJSTORa
2、rchiveindicatesyouracceptanceoftheTerms&ConditionsofUse,availableat.http://www.jstor.org/page/info/about/policies/terms.jsp.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigitalarchive.Weuse
3、informationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org..AppliedProbabilityTrustiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoJournalofAppliedProbability.http://www
4、.jstor.orgThiscontentdownloadedfrom117.28.251.222onFri,8Nov201306:01:09AMAllusesubjecttoJSTORTermsandConditionsJ.Appl.Prob.8,745-756(1971)PrintedinIsrael?AppliedProbabilityTrust1971THETWO-DIMENSIONALPOISSONPROCESSANDEXTREMALPROCESSESJAMESPICKANDSIII,UniversityofPennsy
5、lvaniaAbstractInrecentyearsmanyapplicationsofprobabilitytheoryhaveinvolvedsuchconceptsasrecords,inter-recordtimesandextremeorderstatistics.Theresultshavegenerallybeenprovedbydiversemethods.Inthepresentworkaunifyingstructureispresented,whichmakespossiblethesimplifi-cat
6、ionandextensionofsomeoftheseresults.Theapproachtakenistoplaceallrelevantprocessesonthesamesamplespace.Theunderlyingsamplespaceisahomogeneoustwo-dimensionalPoissonprocess.1.IntroductionManyoftherecentdevelopmentsinprobabilitytheoryhaveinvolvedsimpli-ficationbymeansofau
7、nifyingtheory.Historicallymostoftheclassicallimittheoremswereprovenseparatelyandbydiversemethods.Usefulexamplesarethearcsinelaws,andtheKolmogorov-Smirnovtheorems.Themostprominentgeneralmethodofunifyingresultsisinherentinthestudyoftheweakconvergenceofmeasuresonmetricsp
8、aces(seeProhorov[14],Billingsley[4],andParthasara-thy[13]).Anothermethodinvolvesplacingdifferentstochasticprocessesonthesame
