混合相依隨機(jī)變量序列極限理論的若干結(jié)果.pdf

1、廣西師范大學(xué)碩士學(xué)位論文混合相依隨機(jī)變量序列極限理論的若干結(jié)果姓名：蔣遠(yuǎn)營(yíng)申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計(jì)指導(dǎo)教師：吳群英20080301AbstractLimittheyisoneofthekeybranchesofProbabilitytheyalsotheimptantfoundationofotherbranches.TheresearchpurposeaboutrecentLimittheyistoweakenther

2、estrictionsofindependencetocustomizethemtorealityfeasieridentificationapplication.Butconsideredtheircomplexityenmousproblemshasnotbeenfingeredout.Inthispapersomeproblemsarestudiedsomeresultsareobtainedasfollowsbasedonana

3、lyzingtheiracters.1.Givensomeprobabilityexponentialinequalitiesmomentinequalityofnegativelydependentromsequenceweapplytheseinequalitiestostudyalmostsureconvergence.Asaresultweextendsomealmostsureconvergencetheemsfindepen

4、dentromvariablestothecaseofnegativelydependentromvariablesWestudythecompleteconvergencefnegativelydependentromvariables.Asaresultweextendssomecompleteconvergencetheemsfindependentromvariablestothecaseofnegativelydependen

5、tromvariableswithoutnecessarilyimposinganyextraconditions.Inthelastsectionofchapter2weapplyobtainsomeinequalitiestodiscusseslogarithmtheemsfnegativelydependentromsequences.AsaresultsomeLawsofLogarithmfNDSequencesareobtai

6、ned.Someresultsofliteraturebecomeintoparticularcaseofourresultsbeimproved.2.Westudythealmostsureconvergencef?ρmixingsequencesofromvariables.AsaresultweimprovethecrespondingresultsofYang(1998)Gan(2004)Wu(2001).weextendthe

7、classicalKhintchineKolmogovconvergencetheemMarcinkiewiczstronglawoflargenumbersthethreeseriestheemthealmostsureconvergencepropertiesetc.findependentsequencesofromvariablesto?ρmixingsequencesofromvariableswithoutnecessari

8、lyaddinganyextraconditionsThenwestudytheweakconvergencecompleteconvergencef?ρmixingromvariablesequences.AsaresulttheclassicalweaklawoflargenumbersBaumKatzcompleteconvergencetheemetc.f?ρmixingsequencesofromvariablesareinv

9、estigated.Theresultsextendgreatlyimprovethecrespondingresultsofliterature.Keywds:Negativelydependentpairwisenegativelyquadrantdependent?ρmixingsequencesprobabilityinequalityalmostsureconvergencestronglawoflargenumbersexp