Related papers: Compactness Criterion for Semimartingale Laws and …
The optimal transport problem has recently developed into a powerful framework for various applications in estimation and control. Many of the recent advances in the theory and application of optimal transport are based on regularizing the…
A convergence theorem for martingales with c\`adl\`ag trajectories (right continuous with left limits everywhere) is obtained in the sense of the weak dual topology on Hilbert space, under conditions that are much weaker than those required…
We study a single-period optimal transport problem on $\mathbb{R}^2$ with a covariance-type cost function $c(x,y) = (x_1-y_1)(x_2-y_2)$ and a backward martingale constraint. We show that a transport plan $\gamma$ is optimal if and only if…
It is known from clever mathematical examples \cite{Ca10} that the Monge ansatz may fail in continuous two-marginal optimal transport (alias optimal coupling alias optimal assignment) problems. Here we show that this effect already occurs…
We consider the transfer operators of non-uniformly expanding maps for potentials of various regularity, and show that a specific property of potentials ("flatness") implies a Ruelle-Perron-Frobenius Theorem and a decay of the transfer…
The Skorokhod embedding problem is to represent a given probability as the distribution of Brownian motion at a chosen stopping time. Over the last 50 years this has become one of the important classical problems in probability theory and a…
We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with…
In this paper, we establish a Kantorovich duality for weak optimal total variation transport problems. As consequences, we recover a version of duality formula for partial optimal transports established by Caffarelli and McCann; and we also…
We introduce a new method for obtaining quantitative convergence rates for the central limit theorem (CLT) in a high dimensional setting. Using our method, we obtain several new bounds for convergence in transportation distance and entropy,…
This paper analyzes the support of the conditional distribution of optimal martingale transport plans in higher dimension. In the context of a distance coupling in dimension larger than 2, previous results established by Ghoussoub, Kim &…
Adapted or causal transport theory aims to extend classical optimal transport from probability measures to stochastic processes. On a technical level, the novelty is to restrict to couplings which are bicausal, i.e. satisfy a property which…
We study the convergence of an $N$-particle Markovian controlled system to the solution of a family of stochastic McKean-Vlasov control problems, either with a finite horizon or Schr\"odinger type cost functional. Specifically, under…
We propose a new weak convergence theorem for martingales, under gentler conditions than the usual convergence in probability of the sequence of associated quadratic variations. Its proof requires the combined use of Skorohod's…
The optimal transport problem with quadratic regularization is useful when sparse couplings are desired. The density of the optimal coupling is described by two functions called potentials; equivalently, potentials can be defined as a…
A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar "monotonicity principles" have found applications in other…
The Kantorovich-Rubinshtein metric is an $L^1$-like metric on spaces of probability distributions that enjoys several serendipitous properties. It is complete separable if the underlying metric space of points is complete separable, and in…
The quadratically regularized optimal transport problem has recently been considered in various applications where the coupling needs to be \emph{sparse}, i.e., the density of the coupling needs to be zero for a large subset of the product…
Entropically regularized optimal transport between probability measures supported on compact subsets of Euclidean space admits a representation as an information projection under moment inequality constraints. Exploiting this structure, I…
In this paper, we establish a regularity theory for the optimal transport problem when the target is composed of two disjoint convex domains. This is an important model in which singularities arise. Even though the singular set does not…
We propose a discrete time formulation of the semi martingale optimal transport problembased on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by Guo et…