關(guān)于任意隨機變量序列的一類強偏差定理.pdf

1、江蘇大學(xué)碩士學(xué)位論文關(guān)于任意隨機變量序列的一類強偏差定理姓名：王豹申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：楊衛(wèi)國20060301江蘇大學(xué)碩士學(xué)位論文ABSTRACTProbabilitytheoryisabranchofmathematicsdealingwitllchancephenomenaandhasclearlydiscerniblelinkswiththerealworldItistheframeworkfoundation

2、sofmanyapplyingsubjectssuchasInformationtheoryMathematicsRisktheoryandInsurancetheoryforActuariesectThestronglimittheoremisoneofthecentralquestionsforstudyingprobabilityT11ispapermainlystudiesstrongdeviationtheoremsS打ong

3、deviationtheorems(alsocalledsmalldeviationtheorems)areatypeofnewtheoremsestablishedbyusingthenotionofthelikelihoodratioIn1989ProfessorLiuWjnfirstappliedartanalytictechniqueinthestudyofaclaSsofstrongdeviationtheoremsforas

4、equenceofrandomvariablesIntherecenttenyears，ProfessorLiuWenandYangWeiguocombinethepureanalyticalmethodswiththetoolsofthegeneratingfunctions，themomentgeneratingfunctions，theconditionalmomentgeneratingfunctions，Laplacetran

5、sf01Tnmartinaglewaysand廿ledifferentiationofthemeasureonanettostudythes廿ongdeviationtheorems，Shannon—McMillantheorems，thes訂onglimittheoremsofthegamblingsystemandarbitrarysequenceofdependentrandomvariablesThispapercontains

6、fourchapters，Inchapter1wein拄oducetherelativebackgroundonthispaperandgivesomesimpleexpressionsoftheworkwhichhavebeenstudiedInchapter2，thenotionoflimitrelativeloglikelihoodratioisintroducedtoinvestigatethestrongdeviationth

7、eoremsforthesequenceofdependantdiscreterandomvariablesInchapter3，weintroducethenotionofsamplerelativeentropyrate，asameasureofthedifferencebetweenthesequenceofrandomvariablesandMarkovchains，tostudyaclaSsofstrongdeviationt

8、heoremsforsequenceofarbitraryrandomvariablesInchapter4，aclassofsmalldeviationtheoremsforfunctionalofsequenceofarbitraryrandomvariablesarediscussedbycomparingbetweenthesequenceofarbitrarydistributionsandthesequenceofindep

9、endentdistributions，ascorollaries，somestrongdeviationtheoremsforthecontinuousanddiscreteareextendedKEYWORDS：strongdeviationtheorem，discretedependentrandomvariablesequence，continuousrandomvariablesequence，arbitraryrandomv