特征函數(shù)的性質(zhì)及其應用.pdf

1、湖北大學碩士學位論文特征函數(shù)的性質(zhì)及其應用姓名：闞興莉申請學位級別：碩士專業(yè)：基礎數(shù)學指導教師：田范基20100401AbstractProbabilitytheoryisabranchofmathematicsdealingwiththestatisticallawofrandomphenomena，itstheoremsandmethodshavebeenwidelyusedinfinance、industryandagricult

2、ure，insurance，medicine，industrialandagriculturalproduction、militaryaffairs、disasterforecasteveninthesocialscienceThedistributionfunctionofrandomvariablecompletelydescribedstatisticalregularityofrandomvariables，butwiththe

3、distributionfunctiontosolvesomeproblems，wehavefoundthatitisnoteasyWiththedevelopmentofprobabilitytheory，wehaveintroducedtheFouriertransformtotheprobabilitytheory，thenthecharacteristicfunctionwasgenerated，withtheonetoonec

4、orrespondence’relationshipbetweencharacteristicfunctionanddistributionfunction，manystudiesofrandomvariableswassimplifiedThispapersummarizesthepropertyofthecharacteristicfunctionsystematically，studysthecharacteristicfunct

5、ionofavarietyofcommondistribution，andgivingthecalculationofnumericalcharacteristicwiththecharacteristicfunctionOtherwise，withtheinversionformulaandtheuniquenesstheoremofthecharacteristicfunction，Idiscussedtheapplicationi

6、nKhintchine’Slawandstronglawoflargenumbers，atthesanletime，withthecharacteristicfunction，IgivetwoimportantprobabilitydistributionsThispaperalsosolvessomedifficultquestionwiththecharacteristicfunction，notthedistributionfun

7、ctionsimplyforexample，Istudythereproducingpropertyofsomecommondistributionofrandomvariables，thatindependentofeachotherwithvarioustypesofdistributionofrandomvariablesandthedistributiontypeisunchangedKeyWords：randomvariabl