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University of Bern Switzerland

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47 pages
Realisability problems Ilya Molchanov University of Bern, Switzerland joint work with Raphael Lachieze-Rey University of Lille and University of Luxembourg I. Molchanov Realisability problems. Lille, Mar-Apr 2011 1

  • expected functionals

  • molchanov realisability problems

  • probability distributionspi

  • all functions

  • bounded continuous functions

  • completely alternating


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I.MlohcnavoRaeliasiblityrpbolme.siLll,eMra-pAr0211RealisabilityproblemsIlyaMolchanovUniversityofBern,SwitzerlandjointworkwithRaphaelLachieze-ReyUniversityofLilleandUniversityofLuxembourg1
Ilanoitcnufraenilasi)!(gE=)g(fybdeicepsyl)g(fgsnoitcnufemosrofylnonevigsifitahW?e"!guforallboundedcontinuousfunctionsgqE!(g)in!fonoitubirtsiDu!sExpectedfunctionalsi2Eecapsnitnemelemodnarasi1102rpA-raM,elliL.smelborpytilibasilaeRvonahcloM.
I.MlohcnavoRaeliasibliClassicalexample(Kellerer1964)I}d,...,1{#IecaebteLstesbusfoylimafniatrGivenprobabilitydistributionsPIonRcard(I),doesthereexistaprobabilitydistributiononRdwhosemarginalsarePI,I$I.tyrpbolme.siLll,eMra-pAr02113
I.MlohcnavoRaeliasibliSolutionNeedexistenceofaprobabilitymeasurePonRdsuchthatf(vI)=vI(x)dP(x)=vI(x)dPI(x)!!forallfunctionsvIthatdependonthecoordinateswithnumbersfromI.ExtendffromfunctionsofthetypevIandtheirlinearcombinationstoallfunctionsvonRd.InordertoensurethattheextensionispositiveneedaivI(x)%0ofrallx&f(v#)=ai!v#(x)=""I!Ityrpbolme.siLll,eMra-pAr0211I!I"vI(x)dPI(x)%0.4