Cayley樹(shù)上非對(duì)稱(chēng)馬氏鏈及任意相依隨機(jī)變量序列強(qiáng)極限定理的若干研究.pdf

1、江蘇大學(xué)碩士學(xué)位論文Cayley樹(shù)上非對(duì)稱(chēng)馬氏鏈及任意相依隨機(jī)變量序列強(qiáng)極限定理的若干研究姓名：董燕申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：楊衛(wèi)國(guó)20091218江蘇大學(xué)碩士畢業(yè)論文ABSTRACTTheresearchofstronglimittheoryplaysanimportantroleinthehistoryofprobabilitytheoryInrecentyears，thestronglimittheoryofran

2、domfieldsontreesanddependentrandomvariablesbecometheresearchHighlightofthescholarsRandomfieldsontreesareapplicationsontreesoftheoryofstochasticprocessanewmathmodel，whichdevelopedfromcodingandencodingproblemininformationt

3、heoryAssumingthereisaprocessⅨ，t∈z)，whethertheappearingfrequencyofstateandstatecoupleobeythestronglawoflargenumbersisthekeyofagoodcodingandencodingmethod，SOthisdomainisalwaysbearesearchingemphasesformanyscholarsInrecentye

4、ars，ProfessorYangWeiguoandhisassociatesextendsomestronglimittheoremsandShannonMcMillantheoremfromclassicalMarkovchainstoMarkovchainsonBethetreesandCayleytreesInthethirdchapterofthisarticle，wefirststudythelocalconvergence

5、theoremforfinitenonsymmetricMarkovchainindexedbyCayleytree，thenobtainsomelimittheoremsforthefrequenciesofoccurrenceofstatesandorderedcouplesofstatesfornonsymmetricMarkovchainindexedbythattree，finallyweobtainthestronglawo

6、flargenumbersandasymptoticequipartitionproperty(AEP)withaeconvergenceforfinitenonsymmetricMarkovchainindexedbythattreeThroughoutthe1950s，theconceptofdependentrandomvariableswasraisedinsomebranchesoftheprobabilitytheoryan

7、dmathematicalstatisticsThehistoryandliteratureonthestronglawoflargenumbersfordependentsummandsisnotnearlyasextensiveandcompleteasitisforthecaseofindependentsummandsLyons(1988)andHuetal(2005，2008)studiedtheconvergenceprop

8、ertiesofsumsofdependentrandomvariablesundersecondmomentorcovariancerestrictionsInthefourthchapterofthisarticle，byusingthegeneral“methodofsubsequence”，whichWasdevelopedbyRajchman，westudythestronglimittheoryfordependentran

9、domvariablesbycontrollingthegrowthratesofPthmomentandcovarianceofthemKeywords：CayleyTree；NonsymmetricMarkovchain；Stronglawoflargenumbers；Asymptoticequipartitionproperty；Martingale；Dependentrandomvariables；Jenseninequalit