Paris Dauphine University

About: Paris Dauphine University is a education organization based out in Paris, France. It is known for research contribution in the topics: Context (language use) & Population. The organization has 1766 authors who have published 6909 publications receiving 162747 citations. The organization is also known as: Paris Dauphine & Dauphine.

A representation result for concave schur concave functions

Abstract: A representation result is provided for concave Schur concave functions on L∞(Ω). In particular, it is proven that any monotone concave Schur concave weakly upper semicontinuous function is the infinimum of a family of nonnegative affine combinations of Choquet integrals with respect to a convex continuous distortion of the underlying probability. The method of proof is based on the concave Fenchel transform and on Hardy and Littlewood's inequality. Under the assumption that the probability space is nonatomic, concave, weakly upper semicontinuous, law-invariant functions are shown to coincide with weakly upper semicontinuous concave Schur concave functions. A representation result is, thus, obtained for weakly upper semicontinuous concave law-invariant functions.

Approximation of the Zakai¨ equation by the splitting up method

Abstract: The objective of this article is to apply an operator splitting method to the time integration of Zakai equation. Using this approach one can decompose the numerical integration into a stochastic step and a deterministic one, both of them much simpler to handle than the original problem. A strong convergence theorem is given, in the spirit of existing results for deterministic problems.

Limit distribution theory for maximum likelihood estimation of a log-concave density

Abstract: We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form $f_0=\exp\varphi_0$ where $\varphi_0$ is a concave function on $\mathbb{R}$. The pointwise limiting distributions depend on the second and third derivatives at 0 of $H_k$, the "lower invelope" of an integrated Brownian motion process minus a drift term depending on the number of vanishing derivatives of $\varphi_0=\log f_0$ at the point of interest. We also establish the limiting distribution of the resulting estimator of the mode $M(f_0)$ and establish a new local asymptotic minimax lower bound which shows the optimality of our mode estimator in terms of both rate of convergence and dependence of constants on population values.

Modified logarithmic Sobolev inequalities and transportation inequalities

Abstract: We present a new class of modified logarithmic Sobolev inequality, interpolating between Poincare and logarithmic Sobolev inequalities, suitable for measures of the type $\exp(-|x|^\al)$ or $\exp(-|x|^\al\log^\beta(2+|x|))$ ($\al\in]1,2[$ and $\be\in\dR$) which lead to new concentration inequalities. These modified inequalities share common properties with usual logarithmic Sobolev inequalities, as tensorisation or perturbation, and imply as well Poincare inequality. We also study the link between these new modified logarithmic Sobolev inequalities and transportation inequalities.

Deformable models for 3-D medical images using finite elements and balloons

Abstract: A 3-D generalization of the balloon model as a 3-D deformable surface, which evolves in 3-D images, is presented It is deformed under the action of internal and external forces attracting the surface toward detected edge elements by means of an attraction potential To solve the minimization problem for a surface, two simplified approaches are shown, defining a 3-D surface as a series of 2-D planar curves Then the 3-D model is solved using the finite-element method, yielding greater stability and faster convergence This model has been used to segment magnetic resonance images >