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M. Beiglböck:
"Causal transport in discrete time and applications";
Vortrag: Skorokhod embeddings, Martingale Optimal Transport and their applications, University of Oxford, UK (eingeladen); 16.03.2016.

Loosely speaking, causal transport plans are a relaxation of adapted processes in the same sense as Kantorovich transport plans extend Monge-type transport maps. The corresponding causal version of the transport problem has recently been introduced by Lassalle. Working in a discrete time setup, we establish a dynamic programming principle (DPP) that links the causal transport problem to the transport problem for general costs recently considered by Gozlan et al. Based on this DPP, we give conditions under which the Knothe-Rosenblatt coupling can be viewed as a causal analogue to the Brenier map. As an application we establish functional inequalities for the random walk. These estimates provide Talagrand-type inequalities for the nested distance of stochastic processes and are asymptotically equalities as the number of steps tends to $\infty$.
(based on joint work of J. Backhoff, Y. Lin, A. Zalashko)

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