漸近循環(huán)馬氏鏈的強(qiáng)極限定理.pdf

1、江蘇大學(xué)碩士學(xué)位論文漸近循環(huán)馬氏鏈的強(qiáng)極限定理姓名：鐘萍萍申請(qǐng)學(xué)位級(jí)別：碩士專(zhuān)業(yè)：系統(tǒng)工程指導(dǎo)教師：楊衛(wèi)國(guó)20091218江蘇大學(xué)碩士學(xué)位論文ABSTRACTProbabilitytheoryisawidelyapplicabledisciplineItistheframeworkfoundationsofmanyapplyingsubjectsThestronglimittheoremisoneofthecentralquestion

2、sforstudyingprobabilityMarkovprocessisanimportantstochasticprocessIthasprofoundtheoreticalfundamentandextensiveappliedareaThelimittheoryforMarkovchainsisoneofthebasicareasonMarkovprocesses’researchForthelimittheoryforhom

3、ogeneousMarkovchains，manyresultshavebeenobtained，whicharematureenoughtoformacompletetheoreticalsystemForthelimittheoryfornonhomogeneousMarkovchains，researchershavedonemuchworkinrecentyears，suchasYangandLiu’Sworkonthelimi

4、ttheoremsfornonhomogeneousMarkovchainsSincethecasethatthetransitionmatricesofnonhomogeneousMarkovchainsareasymptoticcircularoftenappearsinpracticaluse，theresearchonthestronglimittheoremsforasymptoticcircularMarkovchainsh

5、asgreattheoreticalandpracticalsignificancesThepurposeofthispaperistostudythestronglawoflargenumbersforasymptoticcircularMarkovchainsandtheasymptoticequipartitionpropertyforasymptoticcircularMarkovchains，whichisamorecommo

6、ncaseofnonhomogeneousMarkovchainsinreallifeInthispaperwefirstintroducethedefinitionofasymptoticcircularMarkovchainsThenbyapplyingthelimitpropertyfordualfunctionsofnonhomogeneousMarkovchains，thestronglimittheoremonthefreq

7、uenciesofoccurrenceofstatesforasymptoticcircularMarkovchainsisestablished，andthestronglawoflargenumbersonthefrequenciesofoccurrenceofstatesforasymptoticcircularMarkovchainsisobtainedFinallywegivetheasymptoticequipartitio

8、npropertyforasymptoticcircularMarkovchainsTheseofferatheoreticalbasisfortheapplicationsofasymptoticcircularMarkovchainsinreallifeKEYWORDS：asymptoticcircularMarkovchains；occurredfrequencyofstates；stronglawoflargenumbers；e