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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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Table of 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.