一类特殊非齐次树上马氏链场的强极限性质论文

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T"B}~bi!1/℄~r7}mySOMESTRONGLIMITPROPERTIESFORMARKOVFIELDSONASPECIALNON-HOMOGENEOUSTREESABSTRACTRandomfieldsontreesareapplicationsofRandomProcesstheo

10、ryontrees,MarkovchainfieldsaretheMarkovchainsindexedbytreeindex.Markovrandomfieldstheoryisoneofbranchesofprobabilitytheorydevelopedre-cently,andthestronglimittheoremsofMarkovchainsfieldsisalsoitsimpor-tantcompontentpart.ProfessorLiuWenfirstlyintroducedhisanalytictechniquestothestudythelimit

11、theoremsofMarkovchainfieldsontrees.Inthechap-tertwoofthepaper,wefirstlyconstructaclassofspecialnon-homogeneoustreesTα0,α1,···,αr−1,usingthemethodsofanalytictechniquesofLiuWen,westudythelimitpropertiesofMarkovchainfieldsonthespecialnon-homogeneoustreesTα0,α1,···,αr−1,weobtainedsomestronglim

12、ittheoremsandintroductionsonthefrequenciesofstates,theorderedcouplestates,andther-tupleofstatesset(i0,i1···,ir−1).TherecurrenceofMarkovchainfieldsontreesgivesusanewdescriptionoftherulesofappearenceofstatekinanotherattitudes.Inthefirstsectionofthechapterthree,usingtheMartingalemethods,west

13、udytherecurrenceofMarkovchainfieldsontrees,andweobtainasufficientconditionforthenon-recurrence,thestrongrecurrenceoftheMarkovchainontreesonconditionthatthestatesetisfinite.Inthesecondsectionofthechapterthree,westudytherayrecurrenceofMarkovchainfieldsonCayleytreeswithoutconfiningtheinitialstat

14、ex0.Inthelastchapter,wesummedupwhatwehavedoneinthepaper.KEYWORDS:Randomfields,Non-homogeneoustrees,Stronglimittheorem,Martingale,Recurrence,Markovchainsii原创性声明本人郑重声明：所呈交的学位论文，是本人在导师指导下，进行研究工作所取得的成果。除文中已经注明引用的内容外，本学位论文的研究成果不包含任何他人创作的、已公开发表或者没有公开发表的作品的内容。对本论文所涉及的研究工作做出贡献的其他个人和集体，均