158 citations · 209 across the 10 of their papers we have counts for
14 papers
On absolutely continuous curves in the Wasserstein space over R and their representation by an optimal Markov process
Charles Boubel, Nicolas Juillet
Let = (t)tR be a 1-parameter family of probability measures on R. In [11] we introduced its ``Markov-quantile''process: a process X= (Xt)tR that resembles as much…
Instability of Martingale optimal transport in dimension d 2
Martin Brückerhoff, Nicolas Juillet
Stability of the value function and the set of minimizers w.r.t. the given data is a desirable feature of optimal transport problems. For the classical Kantorovich transport proble…
Shadow martingales -- a stochastic mass transport approach to the peacock problem
Martin Brückerhoff, Martin Huesmann, Nicolas Juillet
Given a family of real probability measures increasing in convex order (a peacock) we describe a systematic method to create a martingale exactly fitting the marg…
SubRiemanniann structures do not satisify Riemannian Brunn--Minkowski inequalities
Nicolas Juillet
We prove that no Brunn--Minkowski inequality from the Riemannian theories of curvature-dimension and optimal transportation can by satisfied by a strictly subRiemannian structure.…
A Coupling Proof of Convex Ordering for Compound Distributions
Jean Bérard, Nicolas Juillet
In this paper, we give an alternative proof of the fact that, when compounding a nonnegative probability distribution, convex ordering between the distributions of the number of su…
On a solution to the Monge transport problem on the real line arising from the strictly concave case
Nicolas Juillet
It is well-known that the optimal transport problem on the real line for the classical distance cost may not have a unique solution. In this paper we recover uniqueness by consider…
On A Mixture Of Brenier and Strassen Theorems
Nathael Gozlan, Nicolas Juillet
We give a characterization of optimal transport plans for a variant of the usual quadratic transport cost introduced in [33]. Optimal plans are composition of a deterministic trans…
The Markov-quantile process attached to a family of Marginals
Charles Boubel, Nicolas Juillet
Let = (t)tR be any 1-parameter family of probability measures on R. Its quantile process (Gt)tR : ]0, 1[ RR, given by Gt() = inf{x R : t(…
Couplings in distance of two Brownian motions and their L{é}vy area
Michel Bonnefont, Nicolas Juillet
We study co-adapted couplings of (canonical hypoelliptic) diffu-sions on the (subRiemannian) Heisenberg group, that we call (Heisenberg) Brow-nian motions and are the joint laws of…
Shadow couplings
Mathias Beiglboeck, Nicolas Juillet
A classical result of Strassen asserts that given probabilities on the real line which are in convex order, there exists a \emph{martingale coupling} with these marginals, i…
Pliability, or the whitney extension theorem for curves in carnot groups
Nicolas Juillet, Mario Sigalotti
The Whitney extension theorem is a classical result in analysis giving a necessary and sufficient condition for a function defined on a closed set to be extendable to the whole spa…
Smoothing and non-smoothing via a flow tangent to the Ricci flow
Matthias Erbar, Nicolas Juillet
We study a transformation of metric measure spaces introduced by Gigli and Mantegazza consisting in replacing the original distance with the length distance induced by the transpor…
Stability of the shadow projection and the left-curtain coupling
Nicolas Juillet
The (left-)curtain coupling, introduced by Beiglböck and the author is an extreme element of the set of "martingale" couplings between two real probability measures in convex order…
On a problem of optimal transport under marginal martingale constraints
Mathias Beiglböck, Nicolas Juillet
The basic problem of optimal transportation consists in minimizing the expected costs by varying the joint distribution where the marginal dis…