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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2310.20402 |
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| _version_ | 1866916773231591424 |
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| author | Schrott, Stefan Toneian, Daniel |
| author_facet | Schrott, Stefan Toneian, Daniel |
| contents | Strassen established that there exists a two step martingale with marginal distributions $μ$, $ν$ if and only if $μ$, $ν$ are in convex order. Recently Choné-Gozlan-Kramarz obtained a transport characterization of the stochastic order defined by convex positively 1-homogeneous functions, in the spirit of Strassen's theorem under certain technical assumptions. In this note we prove the Choné-Gozlan-Kramarz result in full generality. We also observe that the restriction of the result to the case where $μ, ν$ are supported on a half space is equivalent to Strassen's classical theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_20402 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Strassen's Theorem for support functions Schrott, Stefan Toneian, Daniel Probability Strassen established that there exists a two step martingale with marginal distributions $μ$, $ν$ if and only if $μ$, $ν$ are in convex order. Recently Choné-Gozlan-Kramarz obtained a transport characterization of the stochastic order defined by convex positively 1-homogeneous functions, in the spirit of Strassen's theorem under certain technical assumptions. In this note we prove the Choné-Gozlan-Kramarz result in full generality. We also observe that the restriction of the result to the case where $μ, ν$ are supported on a half space is equivalent to Strassen's classical theorem. |
| title | On Strassen's Theorem for support functions |
| topic | Probability |
| url | https://arxiv.org/abs/2310.20402 |