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| HAL: hal-00379081, version 1 |
| arXiv: 0809.1111 |
| Detailed view |  Export this paper |
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| Electronic Communications in Probability 15 (2010) 124-133 |
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| Measurability of optimal transportation and strong coupling of martingale measures |
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| Joaquin Fontbona 1Hélène Guérin 2 |
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| (2010) |
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| We 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. |
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| 1: | Centro de Modelamiento Matemático (CMM) |
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CNRS : UMI2807 – Universidad de Chile |
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| 2: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 3: | Centre de Mathématiques Appliquées (CMAP) |
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CNRS : UMR7641 – Université de Versailles Saint-Quentin-en-Yvelines – Polytechnique - X |
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| 4: | Modélisation aléatoire de Paris X (MODAL'X) |
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Université Paris X - Paris Ouest Nanterre La Défense |
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| 5: | Ecologie et évolution |
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CNRS : UMR7625 – Université Pierre et Marie Curie [UPMC] - Paris VI – Ecole normale supérieure de Paris - ENS Paris |
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| Subject | : | Mathematics/Probability |
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| Probability |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/0809.1111 |
| hal-00379081, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00379081 | |
| oai:hal.archives-ouvertes.fr:hal-00379081 | |
| From: Dominique Hervé | |
| Submitted on: Monday, 27 April 2009 15:49:25 | |
| Updated on: Wednesday, 20 April 2011 16:14:34 | |
