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dc.contributor.authorÜstünel, A.S.en_US
dc.date.accessioned2016-02-08T10:01:09Z
dc.date.available2016-02-08T10:01:09Z
dc.date.issued2009en_US
dc.identifier.issn0022-1236
dc.identifier.urihttp://hdl.handle.net/11693/22519
dc.description.abstractIn this work we study the necessary and sufficient conditions for a positive random variable whose expectation under the Wiener measure is one, to be represented as the Radon-Nikodym derivative of the image of the Wiener measure under an adapted perturbation of identity with the help of the associated innovation process. We prove that the innovation conjecture holds if and only if the original process is almost surely invertible. We also give variational characterizations of the invertibility of the perturbations of identity and the representability of a positive random variable whose total mass is equal to unity. We prove in particular that an adapted perturbation of identity U = IW + u satisfying the Girsanov theorem, is invertible if and only if the kinetic energy of u is equal to the entropy of the measure induced with the action of U on the Wiener measure μ, in other words U is invertible ifffrac(1, 2) under(∫, W) | u |H 2 d μ = under(∫, W) frac(d U μ, d μ) log frac(d U μ, d μ) d μ . The relations with the Monge-Kantorovitch measure transportation are also studied. An application of these results to a variational problem related to large deviations is also given. © 2009 Elsevier Inc. All rights reserved.en_US
dc.language.isoEnglishen_US
dc.source.titleJournal of Functional Analysisen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.jfa.2009.03.015en_US
dc.subjectCalculus of variationsen_US
dc.subjectEntropyen_US
dc.subjectInvertibilityen_US
dc.subjectLarge deviationsen_US
dc.subjectMalliavin calculusen_US
dc.subjectMonge transportationen_US
dc.titleEntropy, invertibility and variational calculus of adapted shifts on Wiener spaceen_US
dc.typeArticleen_US
dc.departmentDepartment of Mathematicsen_US
dc.citation.spage3655en_US
dc.citation.epage3689en_US
dc.citation.volumeNumber257en_US
dc.citation.issueNumber11en_US
dc.identifier.doi10.1016/j.jfa.2009.03.015en_US
dc.identifier.eissn1096-0783


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