隨機環(huán)境中具有遷移的分枝過程.pdf

1、長沙理工大學碩士學位論文隨機環(huán)境中具有遷移的分枝過程姓名：艾俊勇申請學位級別：碩士專業(yè)：概率論和數(shù)理統(tǒng)計指導教師：李應求20080401ABSTRACTItiswellknown，Branchingprocesswithmigrationinrandomenvironmentsthatdevelopedinrecentyearsisoneofmostimportantstochasticprocessesitsapplicationsp

2、readsdomainandSOonindustry，agriculture，economy，insurance，biologymedicine，projecttechnologyandsocialsciencesThekeyquestionfortheinfluenceofabranchingprocesswithmigrationisthetransitionmatrix，alsocalledittheenvironmentofth

3、ebranchingprocesswithmigrationAsthedirectpositivenaturalenvironmenthasrandomness，alsomayclassicalthebranchingprocesswithmigrationinenvironmentrandomization，obtainsthebranchingprocesswithmigrationinrandomenvironment，theab

4、breviationisBPMRE，accordingtotheenvironmentreliesonthetime，thespace，thetimeandspaceBPMREalsomaydivideintotheBPMREreliesontime，BPMREreliesonspace，BPMREreliesonthetimeandspaceThisarticlefirststudiesintothebranchingprocessw

5、ithmigration，laterstudiesthebranchingprocesswithimmigration，(BPRME)，finallydiscussedthetimesequenceestimatorfortheBPIREAftertheenvironmentrandomization，verymoreresultsinclassicsenvironmentmaybemadesimplepromoted，someactu

6、allyneedstodomassiveworksThispapermainlyissummarizestheworkoftheaspectpredecessorthepaperisdividedintothreeparts：ThefirstpartintroducedthedevelophistoryandtheresearchinpresentsituationfortheBPMREandtheBPIME’Thesecondpart

7、studiedthepropertyoftheBPMRE：theMarkovproperty，momentestimator，thelimitpropertyandtheextinctionThethirdpartusestheassistancestructuremethod，structureastochasticprocesswhichhasthesamedistributionwiththeBPIRE；discussedthec

8、orrelatedprobabilitycharacte“sticfunction；laterobtainsthemomentestimateanditslimitdistributionfortheimmigrationinstationaryergodicenvironment；finally，havethelimittheoremwithstationaryergodicenvironment；andtheconvergencer