Institut Élie Cartan de Lorraine

About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Stochastic differential equation. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.

From invariance principles to a class of multifractional fields related to fractional sheets

Abstract: In this paper, we study some invariance principles where the limits are Gaussian random fields sharing many properties with multifractional Brownian sheets. In particular, they satisfy the same type of self-similarity and Holder regularity properties. We also extend the invariance principles mentioned above in a stable setting.

Points entires au voisinage d'une courbe plane de classe {$C^n$}, II

Abstract: Dans la methode des differences divisees pour majorer le nombre de points entiers au voisinage d'une courbe, Filaseta et Trifonov (1996) ont introduit un argument de divisibilite qui s'applique lorsque le voisinage considere est tres fin. Nous approfondissons cet argument et l'adaptons au cas plus general ou le voisinage n'est plus necessairement aussi fin. Le probleme se complique alors par l'apparition des arcs majeurs, deja rencontres par les auteurs dans un article precedent (1995).

On the time evolution of Bernstein processes associated with a class of parabolic equations

Abstract: In this article dedicated to the memory of Igor D. Chueshov, I first summarize in a few words the joint results that we obtained over a period of six years regarding the long-time behavior of solutions to a class of semilinear stochastic parabolic partial differential equations. Then, as the beautiful interplay between partial differential equations and probability theory always was close to Igor's heart, I present some new results concerning the time evolution of certain Markovian Bernstein processes naturally associated with a class of deterministic linear parabolic partial differential equations. Particular instances of such processes are certain conditioned Ornstein-Uhlenbeck processes, generalizations of Bernstein bridges and Bernstein loops, whose laws may evolve in space in a non trivial way. Specifically, I examine in detail the time development of the probability of finding such processes within two-dimensional geometric shapes exhibiting spherical symmetry. I also define a Faedo-Galerkin scheme whose ultimate goal is to allow approximate computations with controlled error terms of the various probability distributions involved.

Nondispersal and Density Properties of Infinite Packings

Abstract: This article is motivated by an optimization problem arising in Biology. Interpretingthe eggs arrangements (packings) in the brood chamber as results from an optimization process, weare led to look for packings that are at the same time the most possible dense and non-dispersed. Wefirst model this issue in terms of an elementary shape optimization problem among convex bodies,involving their inradius, diameter and area. We then solve it completely, showing that the solutionsare either particular hexagons or a symmetric 2-cap body, namely the convex hull of a disk and twopoints lined-up with the center of the disk.

Linear multifractional multistable motion: LePage series representation and modulus of continuity

Abstract: In this paper, we obtain an upper bound of the modulus of continuity of linear multifractional multistable random motions. Such processes are generalizations of linear multifractional alpha-stable motions for which the stability index alpha is also allowed to vary in time.