University of Bern Switzerland

Ilya Molchanov

Description

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

Informations

• Publié par: profil-urra-2012
• Nombre de lectures: 14
• Langue: English

Extrait

I.MlohcnavoRaeliasiblityrpbolme.siLll,eMra-pAr0211 Realisabilityproblems IlyaMolchanov UniversityofBern,Switzerland jointworkwithRaphaelLachieze-Rey UniversityofLilleandUniversityofLuxembourg 1

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I.MlohcnavoRaeliasibli ❏ Classicalexample(Kellerer1964) I} d,...,1 {# I ecaebteLstesbusfoylimafniatr ❏ Givenprobabilitydistributions P I on R card(I) ,doesthereexista probabilitydistributionon R d whosemarginalsare P I , I $I . tyrpbolme.siLll,eMra-pAr0211 3

I.MlohcnavoRaeliasibli Solution ❏ Needexistenceofaprobabilitymeasure P on R d suchthat f(v I )=v I (x)d P (x)=v I (x)d P I (x) !! forallfunctions v I thatdependonthecoordinateswithnumbersfrom I . ❏ Extend f fromfunctionsofthetype v I andtheirlinearcombinationsto allfunctions v on R d . ❏ Inordertoensurethattheextensionispositiveneed a i v I (x) % 0 ofrall x & f(v # )=a i ! v # (x)= "" I! I tyrpbolme.siLll,eMra-pAr0211 I !I " v I (x)d P I (x) % 0. 4