可交換與按行可交換模糊集值隨機(jī)變量的強(qiáng)大數(shù)定律.pdf

1、北京工業(yè)大學(xué)碩士學(xué)位論文可交換與按行可交換模糊集值隨機(jī)變量的強(qiáng)大數(shù)定律姓名：韓小琴申請(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：李壽梅20050501北京工業(yè)大學(xué)理學(xué)碩士學(xué)位論文AbstractTheaimofthisthesisistoprovestronglawsoflargenumbersforarraysofBanachspacevaluedfuzzyrandomsets，whichareexchangeableorroww

2、iseexchangeableSofar，manyconvergenceresultsareconcernedwithindependentandidenticallydistributed(1iD)fuzzyrandomsetsButinthispaper，weassumethatthefuzzyrandomsetsareomyidenticallydistributed，butnotindependentOntheotherhand

3、，deFinetti’Stheoremguaranteesthatforasequenceofexchangeablerandomsets，thereexistssome盯fieldsuchthatthesequenceofrandomsetsundertheconditionofthe口一fieldhasconditionalliDpropertySothebasicstructurestatedindeFinetti’Stheore

4、mmakesthesequenceofexchangeablefuzzyrandomsetsundersomeconditionshaveconvergenceproperties，thatissimilartothesequenceofIIDrandomsetsWegivetheproofsofstronglawsoflargenumbersfor“riysofBanachspacevaluedfuzzyrandomsets，whic

5、hareexchangeableOrrow—wiseexchangeable，inthesenseoftheextendedHausdorffmetricHo。ratherthaninthesenseofHl(c￡【14]，【15])TheconvergencerespecttoHo。impliestheconvergencerespecttoH1Toprovethestronglawsoflargenumbersoffuzzyrand

6、omsetsrespecttoHooweemploytheimportanttechnique一“Sandwich’’methodaswellastheequivalentpropositionsofrandomsetswhichareexchangeableThe“Sandwich”methodpresentsansimpleapproachtodiscussconvergencetheoremsoffuzzyrandomsetsin

7、thesenseofH。。Inaddition，theaverageofrmldomsetswhichareexchangeablecanberepresentedastheconditionalexpectationandthisrepresentationtogetherwiththeusefulreversemartingaleinequalky32“ei11dispensabilityinproofsofstronglawsof