Timeline for Does strong stochastic ordering exist?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 8, 2023 at 9:29 | comment | added | SBF | Let's say the coupling of $\mu$ and $\nu$ gives almost all the mass to the diagonal with just a little bump under it. They will satisfy the stochastic ordering, but how their neighborhoods will happen to satisfy it as well? | |
| Nov 6, 2023 at 23:03 | comment | added | Jinxiang Yao | Yes, I found some references to Infinite Wasserstein Distance, that helped me a lot in understanding its difference with $W_p$, especially their essential difference here whether the strong stochastic order exists. That's really interesting. Many thanks! | |
| Nov 5, 2023 at 13:05 | comment | added | Martin Hairer | @JinxiangYao It seems that this distance also goes under the name of $\infty$-Wasserstein distance which makes sense. This may help when looking for literature. | |
| Nov 4, 2023 at 19:52 | vote | accept | Jinxiang Yao | ||
| Nov 4, 2023 at 19:21 | comment | added | Jinxiang Yao | Thank you so much! The construction is very interesting! For compactly supported probability measure, this metric can avoid the explosive growth of support. So, for example, the probability measure $\mu$ supported in [0,1] and $\nu$ supported in [2,3], and their small neighborhood under this metric can meet the strong order requirement. | |
| Nov 4, 2023 at 10:22 | history | answered | Martin Hairer | CC BY-SA 4.0 |