资源描述：
《Galton-Watson Processes in Varying Environments.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、Galton-WatsonProcessesinVaryingEnvironmentsAuthor(s):PeterJagersSource:JournalofAppliedProbability,Vol.11,No.1(Mar.,1974),pp.174-178Publishedby:AppliedProbabilityTrustStableURL:http://www.jstor.org/stable/3212594.Accessed:07/11/201305:35YouruseoftheJSTOR
2、archiveindicatesyouracceptanceoftheTerms&ConditionsofUse,availableat.http://www.jstor.org/page/info/about/policies/terms.jsp.JSTORisanot-for-profitservicethathelpsscholars,researchers,andstudentsdiscover,use,andbuilduponawiderangeofcontentinatrusteddigit
3、alarchive.Weuseinformationtechnologyandtoolstoincreaseproductivityandfacilitatenewformsofscholarship.FormoreinformationaboutJSTOR,pleasecontactsupport@jstor.org..AppliedProbabilityTrustiscollaboratingwithJSTORtodigitize,preserveandextendaccesstoJournalof
4、AppliedProbability.http://www.jstor.orgThiscontentdownloadedfrom58.60.63.199onThu,7Nov201305:35:03AMAllusesubjecttoJSTORTermsandConditionsJ.Appl.Prob.11,174-178(1974)PrintedinIsrael?AppliedProbabilityTrust1974GALTON-WATSONPROCESSESINVARYINGENVIRONMENTSPE
5、TERJAGERS,GothenburgUniversity,SwedenAbstractGalton-Watsonprocesseswherethereproductionofindividualsindifferentgenerationscanhavedifferentdistributionsretainmanycharacteristicfeaturesofclassicalprocesses.GALTON-WATSONBRANCHINGPROCESS;RANDOMENVIRONMENT;DI
6、FFUSIONAPPROXIMATIONBehindditffusionapproximations[6],transitionphenomena[4],[8],[9],andrandomenvironments[1],[7],[10]forGalton-WatsonbranchingprocesseslurkstheideaofaGalton-Watsonprocesswherethereproductionmechanism,thoughnotrandom,neednotstaythesamegen
7、erationaftergeneration.Suchaprocessisdefinedastheclassicalone,butwiththenumberofchildrenofindividualsinthenthgenerationhavingareproductiongeneratingfunction4,,n(s)==pksP.k=OIfz,thendenotesthenumberofindividualsingenerationnandzo=1,z,hasprobabilitygenerat
8、ingfunctionfn=40oo0o...o,n-,.AfirstresultisamerereformulationofatheorembyChurchonthecompositionofgeneratingfunctions.See[3]or[1].(Theformulationtherecontainstheunnecessaryrestrictionthatall)i(s)~sandtheproofaminorflaw:-lpn
