On absolutely continuous curves in the Wasserstein space over R and their representation by an optimal Markov process

Charles Boubel, Nicolas Juillet

Let $\mu$ = ($\mu$t)t$\in$R be a 1-parameter family of probability measures on R. In [11] we introduced its ``Markov-quantile''process: a process X= (Xt)t$\in$R that resembles as much…