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.

Equations d'évolution stochastiques dans les espaces de Banach : unicités abstraites, propriété de Markov forte, équations hyperboliques

Abstract: Ce travail comporte quatre chapitres sur les equations d'evolution semilineaires stochastiques (EDPS) dans des espaces de Banach. Le premier chapitre traite des diverses notions d'unicite et d'existence (telles que l'unicite trajectorielle, l'unicite en loi, l'existence forte et faible) et des relations entre elles. Nous construisons d'une maniere differente l'integrale stochastique dans des espaces de Banach, et nous demontrons l'inegalite de Burkholder, le theoreme de Fubini, le theoreme de Chojnowska-Michalik et le theoreme de Girsanov. Nous demontrons aussi des theoremes de conservation de loi pour des integrales de Bochner, des integrales stochastiques et des selecteurs mesurables. Le deuxieme chapitre traite des representations browniennes de martingales locales cylindriques banachiques et du probleme de martingale en dimension infinie. Nous utilisons ces resultats pour demontrer le role de la notion de " bien-pose " et le fait que l'existence faible et l'unicite en loi de l'equation en question entrainent la propriete de Markov forte des solutions. Le troisieme et le quatrieme chapitre concernent des EDPS hyperboliques de second ordre par rapport a un processus de Wiener spatialement homogene. Plus precisement, nous donnons des conditions suffisantes sur les coefficients entrainant l'existence globale des solutions fortes et faibles, et nous demontrons que les solutions se propagent a vitesse finie.

The contact process with aging

Abstract: In this article, we introduce a contact process with aging: in this ge- neralization of the classical contact process, each particle has an integer age that inuences its ability to give birth. We prove here a shape theorem for this process conditioned to survive. In order to establish some key exponential decays, we adapt the Bezuidenhout and Grimmett (1990) construction to build a coupling between our process and a supercritical oriented percolation. Our results also apply to the two-stage contact process introduced by Krone (1999).

Merging costs for the additive Marcus-Lushnikov process, and Union-Find algorithms

Abstract: Starting with a monodisperse configuration with $n$ size-1 particles, an additive Marcus-Lushnikov process evolves until it reaches its final state (a unique particle with mass $n$). At each of the $n-1$ steps of its evolution, a merging cost is incurred, that depends on the sizes of the two particles involved, and on an independent random factor. This paper deals with the asymptotic behaviour of the cumulated costs up to the $k$th clustering, under various regimes for $(n,k)$, with applications to the study of Union--Find algorithms.

The non-linear sewing lemma III: Stability and generic properties

Abstract: Solutions of Rough Differential Equations (RDE) may be defined as paths whose increments are close to an approximation of the associated flow. They are constructed through a discrete scheme using a non-linear sewing lemma. In this article, we show that such solutions also solve a fixed point problem by exhibiting a suitable functional. Convergence then follows from consistency and stability, two notions that are adapted to our framework. In addition, we show that uniqueness and convergence of discrete approximations is a generic property, meaning that it holds excepted for a set of vector fields and starting points which is of Baire first category. At last, we show that Brownian flows are almost surely unique solutions to RDE associated to Lipschitz flows. The later property yields almost sure convergence of Milstein schemes.

Sur un critère de báez-duarte pour l'hypothèse de riemann

Abstract: Define en(t) = {t/n}. Let dN denote the distance in L2(0, ∞; t-2dt) between the indicator function of [1, ∞[ and the vector space generated by e1,…, eN. A theorem of Baez-Duarte states that the Riemann hypothesis (RH) holds if and only if dN → 0 when N → ∞. Assuming RH, we prove the estimate