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dc.contributor.authorBouchard, Bruno
dc.date.accessioned2009-09-09T13:53:38Z
dc.date.available2009-09-09T13:53:38Z
dc.date.issued2005
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/1529
dc.language.isoenen
dc.subjectPartial orderen
dc.subjectProbabilityen
dc.subjectBipolar theoremen
dc.subjectConvex analysisen
dc.subject.ddc519en
dc.titleA version of the G-conditionial bipolar theorem in L0(Rd;P)en
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenMotivated by applications in financial mathematics, Ref. 3 showed that, although $$L^{0}(\mathbb{R}_{+}; \Omega, {\cal F}, \mathbb{P})$$ fails to be locally convex, an analogue to the classical bipolar theorem can be obtained for subsets of $$L^{0}(\mathbb{R}_{+}; \Omega, {\cal F}, \mathbb{P})$$ : if we place this space in polarity with itself, the bipolar of a set of non-negative random variables is equal to its closed (in probability), solid, convex hull. This result was extended by Ref. 1 in the multidimensional case, replacing $$\mathbb{R}_{+}$$ by a closed convex cone K of [0, infin)d, and by Ref. 12 who provided a conditional version in the unidimensional case. In this paper, we show that the conditional bipolar theorem of Ref. 12 can be extended to the multidimensional case. Using a decomposition result obtained in Ref. 3 and Ref. 1, we also remove the boundedness assumption of Ref. 12 in the one dimensional case and provide less restrictive assumptions in the multidimensional case. These assumptions are completely removed in the case of polyhedral cones K.en
dc.relation.isversionofjnlnameJournal of Theoretical Probability
dc.relation.isversionofjnlvol18en
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2005
dc.relation.isversionofjnlpages439-467en
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s10959-005-3512-yen
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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