Measurability of optimal transportation and strong coupling of martingale measures

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dc.creatorFontbona, Joaquin
dc.creatorGuerin, Helene
dc.creatorMeleard, Sylvie
dc.date2008-09-05
dc.date.accessioned2026-07-07T10:01:15Z
dc.date.available2026-07-07T10:01:15Z
dc.descriptionWe consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability result for this map, with respect to the space variable and to the parameter. The proof needs to establish the measurability of some set-valued mappings, related to the support of the optimal transference plans, which we use to perform a suitable discrete approximation procedure. A motivation is the construction of a strong coupling between orthogonal martingale measures. By this we mean that, given a martingale measure, we construct in the same probability space a second one with specified covariance measure. This is done by pushing forward one martingale measure through a predictable version of the optimal transport map between the covariance measures. This coupling allows us to obtain quantitative estimates in terms of the Wasserstein distance between those covariance measures.
dc.identifierhttps://arxiv.org/abs/0809.1111
dc.identifierhttp://arxiv.org/abs/0809.1111
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168568
dc.subjectProbability
dc.subject49Q20, 60G57
dc.titleMeasurability of optimal transportation and strong coupling of martingale measures
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