Search results for "Transport optimal"

showing 2 items of 2 documents

Convexities and optimal transport problems on the Wiener space

2013

The aim of this PhD is to study the optimal transportation theory in some abstract Wiener space. You can find the results in four main parts and they are aboutThe convexity of the relative entropy. We will extend the well known results in finite dimension to the Wiener space, endowed with the uniform norm. To be precise the relative entropy is (at least weakly) geodesically 1-convex in the sense of the optimal transportation in the Wiener space.The measures with logarithmic concave density. The first important result consists in showing that the Harnack inequality holds for the semi-group induced by such a measure in the Wiener space. The second one provides us a finite dimensional and dime…

Convexité[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM][MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Monge-Ampère equationConvexityMonge problem[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Dimension infinieTransport optimalLogarithmic concave measureWiener spaceEspace de WienerOptimal transportÉquation de Monge-AmpèreMesure logarithmiquement concaveProblème de MongeInfinite dimension
researchProduct

Parallel translations, Newton flows and Q-Wiener processes on the Wasserstein space

2022

- We extend the definition of Lott’s Levi-Civita connection to the Wasserstein space of probability measures having density and divergence. We give an extension of a vector field defined along an absolutely curve onto the whole space so that parallel translations can be introduced as done in differential geometry. In the case of torus, we prove the well-posedness of Lott’s equation for parallel translations.- We prove the well-posedness of the Newton flow equation on the Wasserstein space and show the connections between the relaxed Newton flow equation and the Keller-Segel equation.- We establish an intrinsic formalism for Itô stochastic calculus on the Wasserstein space throughout three k…

Newton's methodÉquation de Dean-KawasakiParallel translationTransport optimalTransport parallèleTransport parallèle stochastiqueDean-Kawasaki equationDistance de WassersteinOptimal transportStochastic parallel translation[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Wasserstein distanceMéthode de Newton
researchProduct