Conditional limit theorems for conditionally linearly negative quadrant dependent random variables..pdf

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1、ConditionallimittheoremsforconditionallylinearlynegativequadrantdependentrandomvariablesDe-MeiYuan&YangXieMonatsheftefürMathematikISSN0026-9255Volume166Number2MonatshMath(2012)166:281-299DOI10.1007/s00605-012-0373-1123Yourarticleisprotectedbycopyrightandallrigh

2、tsareheldexclusivelybySpringer-Verlag.Thise-offprintisforpersonaluseonlyandshallnotbeself-archivedinelectronicrepositories.Ifyouwishtoself-archiveyourwork,pleaseusetheacceptedauthor’sversionforpostingtoyourownwebsiteoryourinstitution’srepository.Youmayfurtherde

3、posittheacceptedauthor’sversiononafunder’srepositoryatafunder’srequest,provideditisnotmadepubliclyavailableuntil12monthsafterpublication.123Author'spersonalcopyMonatshMath(2012)166:281299DOI10.1007/s00605-012-0373-1Conditionallimittheoremsforconditionallylinear

4、lynegativequadrantdependentrandomvariablesDe-MeiYuan·YangXieReceived:25September2010/Accepted:13January2012/Publishedonline:31January2012©Springer-Verlag2012AbstractFromtheordinarynotionoflinearlynegativequadrantdependenceforasequenceofrandomvariables,anewconce

5、ptcalledconditionallylinearlynegativequadrantdependenceisintroduced.Therelationbetweenthetwokindsofdependenceisansweredbyexamples,thatis,thelinearlynegativequadrantdependencedoesnotimplytheconditionallylinearlynegativequadrantdependence,andviceversa.Thefundamen

6、talpropertiesofconditionallylinearlynegativequadrantdependencearedeveloped,whichextendthecorrespondingonesunderthenon-conditioningsetup.Bymeansoftheseproperties,someconditionalexponentialinequalities,conditionallycompleteconvergenceresultsandaconditionalcentral

7、limittheoremstatedintermsofconditionalcharacteristicfunctionsareestablished.KeywordsConditionallylinearlynegativequadrantdependence·Conditionalexponentialtypeinequality·Conditionalindependence·Conditionalstochasticdomination·Conditionallycompleteconvergence·Con

8、ditionalcentrallimittheoremMathematicsSubjectClassification(2000)60F15·60F25CommunicatedbyP.Friz.D.-M.Yuan(B)SchoolofMathematicsandStatistics,ChongqingTechnologyandBusinessUn