• Corpus ID: 250264808

A characterisation of convex order using the 2-Wasserstein distance

  title={A characterisation of convex order using the 2-Wasserstein distance},
  author={Johannes Wiesel and Eric Zhang},
. We give a new characterisation of convex order using the 2-Wasserstein distance W 2 : we show that two probability measures µ and ν on R d with finite second moments are in convex order (i.e. µ (cid:22) c ν ) iff holds for all probability measures ρ on R d with bounded support. Our proof of this result relies on a quantitative bound for the infimum of (cid:82) f dν − (cid:82) f dµ over all 1-Lipschitz functions f , which is obtained through optimal transport duality and Brenier’s theorem. We use… 
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