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- W2035707149 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." @default.
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- W2035707149 date "2010-01-01" @default.
- W2035707149 modified "2023-10-15" @default.
- W2035707149 title "Measurability of optimal transportation and strong coupling of martingale measures" @default.
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- W2035707149 doi "https://doi.org/10.1214/ecp.v15-1534" @default.
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