常返和暫留Markov過程的分類.pdf

1、中文題名堂運麴塹留叢壘然QY過程的盆婁≥乏文題名!魚曼魚!壘i魚壘壘!iQ墜Q￡!!壘墮!i曼墮!壘塾魚!璺壘墜!!曼壘!壘壟壘!kQ!P!Q壁星呈曼曼墨博士后姓名趙斂萱流動站(一級學(xué)科)名稱數(shù)堂班童壓專業(yè)(二級學(xué)科)名稱拯奎途皇隨扭過程途研究工作起始時間2QQ3生3目研究工作期滿時間2QQ5生3屋單位名稱復(fù)旦太堂數(shù)堂壓報告提交日期2QQ生3旦AbstractTransienceandrecurrenceareamongmostimpo

2、rtantconceptsinMarkovprocessesThisthesisconsistsoftwopartsThefirstpartisconcernedwiththeclassificationofrecurrentandtransientrightprocessesFirstly，westudythetransienceandrecurrenceforrightprocesseswithagivenincreasingwei

3、ghtfunctionandcharacterizethembypotentials，excessivefunctionsand1astexittimesoftheprocessSecondly，weinvestigatethepropertiesofrecurrentstatesThirdlywestudytherecurrenceandtransiencewithanydecreasingweightfunction，whichcl

4、assifytherecurrentrightprocessesmorefine堍provethatW—recurrenceisaclasspropertyandgiveadichotomytheoremundertheconditionthatXisirreducibleFourthlytheWtransienceandWrecurrenceforLdvyproceasarestudiedWeuseLdvyexponenttogive

5、anecessityconditionforW—recurrentLdvyprocesseswhichisalsoasufficientconditionforsymmetricLdvyprocessesThesecondpartisdevotedtoclassifythenullrecurrentMarkovchainsmorepreciselyFirstlywecharacterizethefinitenessof屁p‰)Jbyme

6、ansofthe禮一steptransitionprobabilitiesp涮)，where％isthefirstreturningtimetozand訓(xùn)isapositivefunctionsatisfyingsomeconditionsSecondlyweshallstudythereversibleMarkovchainswhichrelatetoelectricnetworksWecharacterizeB(tTM)bythee

7、ffectiveconductanceofthecorrespondingnetworkundersomemodificationandgiveanequivalentconditionforthefinitenessof玩[叫(％)】bytheeffectiveconductancesFinallywegivesomemonotonicitylawsbywhichwemaycomparethereturningspeedoftweve