特征函數(shù)的性質(zhì)及其應(yīng)用.pdf

1、湖北大學(xué)碩士學(xué)位論文特征函數(shù)的性質(zhì)及其應(yīng)用姓名：闞興莉申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)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