Weak optimal transport with unnormalized kernels
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916212825391104 |
|---|---|
| author | Choné, Philippe Gozlan, Nathael Kramarz, Francis |
| author_facet | Choné, Philippe Gozlan, Nathael Kramarz, Francis |
| contents | We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this transport problem. We also obtain dual attainment conditions for some specific cost functions. As a byproduct we obtain a transport characterization of the stochastic order defined by convex positively 1-homogenous functions, in the spirit of Strassen theorem for convex domination. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_16227 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Weak optimal transport with unnormalized kernels Choné, Philippe Gozlan, Nathael Kramarz, Francis Functional Analysis Optimization and Control Probability We introduce a new variant of the weak optimal transport problem where mass is distributed from one space to the other through unnormalized kernels. We give sufficient conditions for primal attainment and prove a dual formula for this transport problem. We also obtain dual attainment conditions for some specific cost functions. As a byproduct we obtain a transport characterization of the stochastic order defined by convex positively 1-homogenous functions, in the spirit of Strassen theorem for convex domination. |
| title | Weak optimal transport with unnormalized kernels |
| topic | Functional Analysis Optimization and Control Probability |
| url | https://arxiv.org/abs/2203.16227 |