一类非齐次树上二重马氏链场的强极限定理

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1、河北工业大学硕士学位论文一类非齐次树上二重马氏链场的强极限定理姓名：姜慧慧申请学位级别：硕士专业：应用数学指导教师：金少华20081201S4ob_mR_"=Yqd2mE.A(gt}6v)?℄&_an-al!gE,tg
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3、RACTDuringthelastdecade,thetreemodelhasattractedagreatdealofinterestamongscientistsfromvariousresearchfieldssuchasphysics,probabilitytheory,informationtheoryetc..Moreover,stochasticprocessindexedbyatreehasbe-comeahottopicinthefieldoftheprobabilitytheoryinrecentyears.Ontheotherhand,thestronglimi

4、ttheoremsisoneofthecentralissuesoftheinternationalprobabilitytheory.Throughconstructingaseriesofmartingales,thispaperappliesDoob'smartin-galeconvergencetheoremtotheresearchofa.e.convergence,givessomestronglimittheoremsfortwoorderedMarkovchainsindexedbyakindofnonhomoge-noustree.Thispaperinclud

5、esfivechapters:Thefirstchapterisintroduction,introducingtheresearchingpurposeandmean-ingsofthispaper,andtheworkthatexisted.Thesecondchapterispreparativeknowledge.Wegivetheconceptofthetreeandthedefinitionofaspecialkindofnon-homogeneoustree.Inthethirdchapter,weintroducetherandomselectionsysteminto

6、thetwo-orderedMarkovchainsonanon-homogeneoustree,andgivesomestronglimittheoremsoftherandomselectionsystemonthetree.Then,wegivesomestronglimittheoremsonthefrequencyofoccurrenceofthestateandtheorderedcoupleofstates.Intheforthchapter,westudythetwoorderedMarkovapproximationtoran-domfieldonthetree.

7、Andweconstructsomestrongdeviationtheoremsonthefrequencyofoccurrenceoftheorderedcoupleofstates,thesetheoremsholdal-mostsurelyunderanyprobabilitymeasure.Inthelastchapter,wesumupwhatwehavedoneinthispaper.KEYWORDS:aspecialkindofnon-homogeneoustre