ρ混合序列若干收敛性质的研究

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3、saroŒÈ;£Ä²þL§;Lp-Âñ.I2Ü“‰Æa¬ÆØ©2013SomeConvergencePropertiesof~-MixingRandomSequencesABSTRACTTheconceptof~-mixingsequenceswasrstintroducedbyBradleyin1990.Bythedenitionof~-mixing,itiseasytoknow~-mixingsequenceissimilarto-mixingsequence,buttheyarequitedierentfrom

4、eachother.Infact,~-mix-ingsequencesismuchweakerthan-mixingsequences.So~-mixingsequencesiscalledtobeweaklymixingbysomeliterature.~-mixingsequenceshavefoundwideapplicabilityinnaturalsciences,socialsciences,engineeringtechnology,mil-itaryscienceandproductionlife.Aswe

5、knowtheconvergencepropertiesof~-mixingsequencecanbeappliedtoanempiricalanalysisofstockpriceindex.Therefore,thelimittheoryandstatisticaltheoryof~-mixingsequencehavere-ceivedwideattentionfrommanyscholars.Themaincontentsofthisthesisarelistedasfollows.Insection1,thistop

6、icdevelopmentbackgroundandbasicknowledgeareintroduced.InSection2,thelimitingbehaviorofmovingaverageprocessunder~-mixingassumptionswasdiscussed.Forexample,thecompletemomentconvergenceofmovingaverageprocessunder~-mixingassumptionswasobtained,whichextendtheresultofLian

7、dZhang(2004)undernegativelyassociatedrandomvariablesto~-mixingrandomvariables.Thepreciseasymptoticsincompletemomentconvergenceofmovingaverageprocessunder~-mixingassumptionswasalsoinvestigated.InSection3,thelimitingbehaviorofthemaximumofpartialsumsunder~-mixingandre

8、sidualCesarointegrabilityassumptionwasestablished.Forexample,under~-mixingandresidualCesarointegrabilityorstronglyresidua