Related papers: Transportation Cost Inequalities for Neutral Funct…
We give a necessary and sufficient condition for transport-entropy inequalities in dimension one. As an application, we construct a new example of a probability distribution verifying Talagrand's T2 inequality and not the logarithmic…
In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices of these transportation problems are of special structure. We observe that the…
In this paper, we study the optimal transport problem induced by separable cost functions. In this framework, transportation can be expressed as the composition of two lower-dimensional movements. Through this reformulation, we prove that…
We study incommensurate fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives and generalized fractional integrals and derivatives. We obtain necessary optimality…
Inequalities between transportation costs and Fisher information are known to characterize certain concentration properties of Markov processes around their invariant measures. This note provides a new characterization of the quadratic…
We propose a discrete time formulation of the semi-martingale optimal transport problem based on multi-marginal entropic transport. This approach offers a new way to formulate and solve numerically the calibration problem proposed by [17],…
This work is devoted to direct mass transportation proofs of families of functional inequalities in the context of one-dimensional free probability, avoiding random matrix approximation. The inequalities include the free form of the…
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Cameron-Martin formula for solutions of a…
The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coefficient. We investigate related Cauchy problems…
In this paper, we introduce a primal-dual algorithm for solving (martingale) optimal transportation problems, with cost functions satisfying the twist condition, close to the one that has been used recently for training generative…
In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an…
We first give a characterization of the L^1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences.…
Explicit sufficient conditions on the hypercontractivity are presented for two classes of functional stochastic partial differential equations driven by, respectively, non-degenerate and degenerate Gaussian noises. Consequently, these…
New transportation cost inequalities are derived by means of elementary large deviation reasonings. Their dual characterization is proved; this provides an extension of a well-known result of S. Bobkov and F. G\"{o}tze. Their tensorization…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
In this paper, we address the numerical solution to the multimarginal optimal transport (MMOT) with pairwise costs. MMOT, as a natural extension from the classical two-marginal optimal transport, has many important applications including…
For a given Lagrangian $L:[0,T]\times M\times M^\ast\rightarrow \mathbb{R}_+$ and probability measures $\mu\in\mathcal{P}(M^\ast)$, $\nu\in \mathcal{P}(M)$, we introduce the stochastic ballistic transportation problems…
We consider dynamical systems that are described by fractional power of coordinates and momenta. The fractional powers can be considered as a convenient way to describe systems in the fractional dimension space. For the usual space the…
We study uncertainty in the dynamics of time-dependent flows by identifying barriers and enhancers to stochastic transport. This topological segmentation is closely related to the theory of Lagrangian coherent structures and is based on a…
A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…