常返和暫留Markov過(guò)程的分類(lèi).pdf

1、中文題名堂運(yùn)麴塹留叢壘然QY過(guò)程的盆婁≥乏文題名!魚(yú)曼魚(yú)!壘i魚(yú)壘壘!iQ墜Q￡!!壘墮!i曼墮!壘塾魚(yú)!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(dòng)站(一級(jí)學(xué)科)名稱(chēng)數(shù)堂班童壓專(zhuān)業(yè)(二級(jí)學(xué)科)名稱(chēng)拯奎途皇隨扭過(guò)程途研究工作起始時(shí)間2QQ3生3目研究工作期滿(mǎn)時(shí)間2QQ5生3屋單位名稱(chēng)復(fù)旦太堂數(shù)堂壓報(bào)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