Optimal transport with some directed distances
In a previous joint paper, the author and Broniatowski introduced a concept of direct distances (also called divergences) between two arbitrary functions, so widening the class of the so-called scaled Bregman distances (divergences). In the present paper the author applies the new concept of direct distances to the case of quantile functions. Next he considers and solves some new optimal transport problems were the cost functions are pointwise such distances. For the entire collection see [Zbl 1482.94007].
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