Related papers: Localisation for constrained transports II: applic…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the…
We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI…
We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…
We provide a pointwise bipolar theorem for liminf-closed convex sets of positive Borel measurable functions on a sigma-compact metric space without the assumption that the polar is a tight set of measures. As applications we derive a…
In recent works - both experimental and theoretical - it has been shown how to use computational geometry to efficently construct approximations to the optimal transport map between two given probability measures on Euclidean space, by…
Based on the multidimensional irreducible paving of De March & Touzi, we provide a multi-dimensional version of the quasi sure duality for the martingale optimal transport problem, thus extending the result of Beiglb\"ock, Nutz & Touzi.…
Two probability distributions $\mu$ and $\nu$ in second stochastic order can be coupled by a supermartingale, and in fact by many. Is there a canonical choice? We construct and investigate two couplings which arise as optimizers for…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
This paper investigates causal optimal transportation problems, in the framework of two Polish spaces, both endowed with filtrations. Specific concretizations yield primal problems equivalent to several classical problems of stochastic…
We establish a variant of Monge--Kantorovich duality for a constrained optimal transport problem with a continuum of agents, a finite set of alternatives, and general linear constraints. As an application, we revisit the large-market model…
We show that a class of Poincar\'e-Wirtinger inequalities on bounded convex sets can be obtained by means of the dynamical formulation of Optimal Transport. This is a consequence of a more general result valid for convex sets, possibly…
We study the Lagrangian formulation of a class of the Monge-Kantorovich optimal transportation problem. It can be considered a stochastic optimal transportation problem for absolutely continuous stochastic processes. A cost function and…
Quantization provides a very natural way to preserve the convex order when approximating two ordered probability measures by two finitely supported ones. Indeed, when the convex order dominating original probability measure is compactly…
Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace's equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in…
We introduce and study the permanence properties of the class of linear transfers between probability measures. This class contains all cost minimizing mass transports, but also martingale mass transports, the Schrodinger bridge associated…
We introduce a technique for the analysis of general spatially coupled systems that are governed by scalar recursions. Such systems can be expressed in variational form in terms of a potential functional. We show, under mild conditions,…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
For probability measures on a complete separable metric space, we present sufficient conditions for the existence of a solution to the Kantorovich transportation problem. We also obtain sufficient conditions (which sometimes also become…