Saved in:
Bibliographic Details
Main Authors: Schrott, Stefan, Toneian, Daniel
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2310.20402
Tags: Add Tag
No Tags, Be the first to tag this record!
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.