Weak Optimal Entropy Transport Problems

Abstract

In this paper, we introduce weak optimal entropy transport problems that cover both optimal entropy transport problems and weak optimal transport problems introduced by Liero, Mielke, and Savaré [27]; and Gozlan, Roberto, Samson and Tetali [20], respectively. Under some mild assumptions of entropy functionals, we establish a Kantorovich type duality for our weak optimal entropy transport problem. We also introduce martingale optimal entropy transport problems, and express them in terms of duality, homogeneous marginal perspective functionals and homogeneous constraints.

36 pages. Minor changes, and one reference is added. We also added Lemma 9 which was suggested by one of the two anonymous referees