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Results tagged with wasserstein-distance
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user 11054
2
votes
Accepted
Unique coupling
The only way this can happen is the situation that you described, where at least one of the measures gives full measure to a single point. In fact, the proof below does not require the two Polish spac …
- 23.2k
3
votes
Accepted
Is there $\varepsilon \in (0, 1)$ such that $\sup_{t \in [0, \varepsilon]} [\ell_t]_\beta < ...
Pick a sequence of functions $g_n$ where (i) $\|g_n\|_\beta=n$ and (ii) $\|g_n-\mathbf 1\|_\infty\le 3^{-n}$. For example
$$
g_n(x)=\begin{cases}
1+n(a_n-x)^\beta&\text{if $0\le x\le a_n$};\\
1&\text{ …
- 23.2k