非齐次树上马乐科夫链场的若干强偏差定理.pdf

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2、eZr½nu°J•“6¶:7uÇàó’ŒÆžÆ?O:a¬Æ‰!;’¶¡:A^êÆØ©Jžm:2011c11Ø©‰Fžm:2011c12Æǃü:àó’ŒÆ‰F”¬ÌR:µ<:2011c12DissertationSubmittedtoHebeiUniversityofTechnologyforTheMasterDegreeofScienceinAppliedMathematicsSOMESTRONGDEVIATIONTHEOREMSFORMARKOVCHAINFIELDSONATREEbyYuHairongSu

3、pervisor:Prof.JinShaohuaDec.2011àó’ŒÆa¬ÆØ©šàgäþê‰Åó

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7、Ñšàgäþm•šàgê¼&˜aShannon-McMillan½n"1oÙÏLEn¦È—ݼꆷšK§‰Ñ˜ašàgäþëYGê¼ó2ÂÙÆXÚ˜ar½n"1ÊÙÏLE·šK‰Ñšàgäþšàgê¼ó‘Å=£VÇNÚ²þ4•5Ÿ"18Ù•(اo(©̇(J"'…c:šàg䧧Shannon-McMillan½n§r½n§ê¼&§šàgê¼ó§‘Å=£VǧNÚ²þišàgäþê‰Åó

8、eZr½nSOMESTRONGDEVIATIONTHEOREMSFORMARKOVCHAINFIELDSONATREEABSTRACTInrecentyears,

9、thetreemodelhasattractedagreatdealofinterestamongscien-tistsfromvariousresearchfieldssuchasphysics,probabilitytheory,informationtheoryetc..Moreover,stochasticprocessindexedbyatreehasbecomeahottop-icinthefieldoftheprobabilitytheoryinrecentyears.Andthestrongdeviationtheoremisoneofthecentralissuesofthei

10、nternationalprobabilitytheory.Inthispaper,throughconstructingnon-negativemartingalesandappliesDoob’smartingaleconvergencetheoremtotheresearchofa:e:convergence,somestrongdeviationtheoremsforMarkovchainfieldsonanon-homogeneoustreearegiven.Thispaperincludessixchapters:Thefirstchapterisintroduction,intro

11、ducingtheresearchingpurposeandmean-ingsofthispaper,andtheworkthatexisted.Thesecondchapterispreparativeknowledge.Wegivetheconceptofthetreeandthedefinitionofaspecialkindofnon-homogeneoustree.Inthethirdchapter,byapplyingtheconceptoftherelativeentropydensityandtherandomconditionentropy,andthroughconstru

12、ctinganappropriatenon-negativemartingale,wegiveShannon-McMillantheoremofmorderednon-homogeneousMarkovinformationsourceonthenon-homogeneoustree.Intheforthchapter,throughconstructingn-elementproductdensityfun