158 citations · 209 across the 10 of their papers we have counts for
9 papers · 1 filter
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…
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…
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…