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Measurability of optimal transportation and strong coupling of martingale measures


 
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1. Title Title of document Measurability of optimal transportation and strong coupling of martingale measures
 
2. Creator Author's name, affiliation, country Joaquin Fontbona; Universidad de Chile
 
2. Creator Author's name, affiliation, country Hélène Guérin; Université Rennes 1
 
2. Creator Author's name, affiliation, country Sylvie Méléard; École Polytechnique
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Measurability of optimal transport. Coupling between orthogonal martingale measures. Predictable transport process.
 
3. Subject Subject classification 49Q20, 60G57
 
4. Description Abstract We consider the optimal mass transportation problem in $\mathbb{R}^d$ with measurably parameterized marginals 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 a specified covariance measure process. This is done by pushing forward the first 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.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Conicyt (Chilean Government)
 
7. Date (YYYY-MM-DD) 2010-04-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1534
 
10. Identifier Digital Object Identifier 10.1214/ECP.v15-1534
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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