隨機非齊次聚合分解過程.pdf

1、上海交通大學博士學位論文隨機非齊次聚合分解過程姓名：胡春華申請學位級別：博士專業(yè)：應用數(shù)學指導教師：韓東20071201ABSTRACTofPhysicistofparticlesystem，SoourresultisveryimportanttothestudyofthemicroscopicmodelsWhenthetotalnumberoftheparticlesNgotoinfi—nite，Weprovethatthedistr

2、ibutionofthenumberofsmall，mediumandlargestclustersconvergetoGaussian，Poissonand1—0distributioninthesupercritical(post—gelation)，respectivelyThispapercontainssixsectionsInsection1，wegivesomeintroductiononallkindsofcoagula

3、tion—fragmentationmodelInsection2，weshowthatthereisauniqueFellerprocesscorrespondingtotheheterogeneouscoagulationfragmentationmodelininfinitedimensionalInsection3，wegiveouttheclosedformoftheinvariantmeasureandsomepropert

4、iesoftheinvariantmeasureoftherandomheterogeneouscoagulation—fragmentationprocessInsection4，weprovethatthehydrodynamiclimitofthetheheterogeneouscoagulation—fragmentationprocessInsection5，weconsidertheasymptoticprobability

5、distributionofsizeofthereversiblerandomheterogeneouscoagulationfragmentationprocessInthelastsection，WelistsomeproblemsontheheterogeneouscoagulationfragmentationmodelwhichWewillcontinuetostudyKEYWORDSCoagulation—fragmenta