@article{ECP1534,
author = {Joaquin Fontbona and Hélène Guérin and Sylvie Méléard},
title = {Measurability of optimal transportation and strong coupling of martingale measures},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {15},
year = {2010},
keywords = {Measurability of optimal transport. Coupling between orthogonal martingale measures. Predictable transport process.},
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.},
pages = {no. 13, 124-133},
issn = {1083-589X},
doi = {10.1214/ECP.v15-1534},
url = {http://ecp.ejpecp.org/article/view/1534}}