非齐次树上马乐可夫链场的若干强大数定律.pdf

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12、NUMBERSFORMARKOVCHAINFIELDSONANON-HOMOGENEOUSTREEABSTRACTMarkovprocessisaveryimportantclassofstochasticprocess.Itplaysanex-traordinaryroleinmanyfields.Duringrecentyears,thetreemodelhasattractedextensiveinterestinthefieldsofphysics,probabilitytheoryandinformationtheo-ryetc..Markovc

13、hainfieldindexedbyatreeisaspecialstochasticfield.Actuallyitisastochasticwalkindexedbyatree.Inrecentyears,stochasticprocessindexedbyatreehasbecomeoneoftheresearchdirectionsforstudyingintheprobabilitytheory.Thestronglawoflargenumbershasbeenoneofthecentralissuesoftheinternationalprob

14、abilitytheory.Byconstructingmartingaledierencesequences,thispaperapplymartingaledierencesequenceconvergencetheoremtogiveandprovesomestronglawsoflargenumbersforMarkovchainfieldsonanon-homogeneoustree.Thecontentsofthispaperisdividedintosixchapters:Thefirstchapterisintroduction,descr

15、ibingtheresearchingpurpose,signifi-canceandtheworkthatexisted.Thesecondchapterispreparativeknowledge.Weintroducetheconceptofthetreeandgivethedefinitionofaspecialkindofnon-homogeneoustree.Inthethirdchapter,wegivemanystrongdeviationlimittheoremsbasedonPoissondistributionforMarkovcha

16、infieldsonanon-homogeneoustree.Intheforthchapter