0000000001198983

AUTHOR

Vincent Nolot

showing 4 related works from this author

Monge Problem on infinite dimensional Hilbert space endowed with suitable Gaussian measure

2014

In this paper we solve the Monge problem on infinite dimensional Hilbert space endowed with a suitable Gaussian measure, that satisfies the Lebesgue differentiation theorem.

Optimization and Control (math.OC)FOS: MathematicsMathematics - Optimization and Control
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Sobolev estimates for optimal transport maps on Gaussian spaces

2012

We will study variations in Sobolev spaces of optimal transport maps with the standard Gaussian measure as the reference measure. Some dimension free inequalities will be obtained. As application, we construct solutions to Monge-Ampere equations in finite dimension, as well as on the Wiener space.

Mathematics::Complex VariablesGaussianProbability (math.PR)Mathematics::Analysis of PDEsGaussian measureSobolev spaceStrong solutionssymbols.namesakeFOS: MathematicssymbolsApplied mathematicsEntropy (information theory)Fisher informationMathematics - ProbabilityAnalysisMathematicsJournal of Functional Analysis
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Optimal transport on the classical Wiener space with different norms

2011

In this paper we study two basic facts of optimal transportation on Wiener space W. Our first aim is to answer to the Monge Problem on the Wiener space endowed with the Sobolev type norm (k,gamma) to the power of p (cases p = 1 and p > 1 are considered apart). The second one is to prove 1-convexity (resp. C-convexity) along (constant speed) geodesics of relative entropy in (P2(W);W2), where W is endowed with the infinite norm (resp. with (k,gamma) norm), and W2 is the 2-distance of Wasserstein.

Mathematics - Functional AnalysisProbability (math.PR)FOS: MathematicsMathematics - ProbabilityFunctional Analysis (math.FA)
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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
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