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Results tagged with wasserstein-distance
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user 8588
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vote
Lipschitz-type inequalities for Markov kernels
Assuming that your distance is convex, the question reduces just to the case when both $\mu$ and $\nu$ are delta measures, and amounts then to the inequality
$$\tag {$\star$}
d(\delta_x,\delta_y) \le …
- 17k
6
votes
Accepted
Wasserstein distance in R^d from one dimensional marginals
There is a result which contains an answer to your question in a somewhat different form. Instead of the transportation metric it uses another metric which metrizes the weak topology in the space of m …
- 4,713
10
votes
Accepted
Upper bound total variation by Wasserstein distance for continuous distance
No. One should realize that the transportation and the total variation distances metrize two quite different topologies. Even if the measures are equivalent (i.e., absolutely continuous with respect t …
- 17k
14
votes
Accepted
Metrization of weak convergence of signed measures
Of course, there are many ways of metrizing the weak topology on $\mathcal M(\Omega)$ by using various tools of functional analysis. However, as it has already been pointed out by Dan, the most natura …
- 17k