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.

Convergence of stochastic gene networks to hybrid piecewise deterministic processes

Abstract: We study the asymptotic behavior of multiscale stochastic gene networks using weak limits of Markov jump processes. Depending on the time and concentration scales of the system we distinguish four types of limits: continuous piecewise deterministic processes (PDP) with switching, PDP with jumps in the continuous variables, averaged PDP, and PDP with singular switching. We justify rigorously the convergence for the four types of limits. The convergence results can be used to simplify the stochastic dynamics of gene network models arising in molecular biology.

Contribution à la notion d'autosimilarité et à l'étude des trajectoires de champs aléatoires.

Abstract: Mes travaux portent essentiellement sur des champs aleatoires qui satisfont une propriete d'autosimilarite globale ou locale, eventuellement anisotrope. Au cours de ces dernieres annees, je me suis concentree sur l'etude de la regularite des trajectoires de tels champs mais aussi de leur simulation, de l'estimation des parametres ou encore de certaines proprietes geometriques (dimension d'Hausdorff). J'ai ete amenee a introduire de nouvelles notions d'autosimilarite : autosimilarite locale pour des champs indexes par une variete et autosimilarite locale anisotrope. Une partie de mes travaux porte sur des series de type shot noise (vitesse de convergence, regularite). Ces series permettent notamment de proposer une methode de simulation pour les champs fractionnaires ou multifractionnaires. Elles nous ont permis d'obtenir une majoration du module de continuite de champs aleatoires anisotropes stables mais sont aussi utiles pour l'etude de champs plus generaux (champs definis par une serie aleatoire conditionnellement sous-gaussienne, champs multi-stables). L'etude de modeles anisotropes est motivee par la modelisation de roches mais aussi de radiographies d'os en vue de l'aide a la detection precoce de l'osteoporose (projet ANR MATAIM). J'ai aussi aborde des questions plus statistiques : estimations des parametres, propriete LAN (Local Asymptotic Normality). Enfin, au sein de l'equipe INRIA BIology Genetics and Statistics, je travaille sur des problematiques tournees vers des applications medicales en collaboration avec des automaticiens. J'ai en particulier travaille sur un algorithme de debruitage en vue d'application a des ECG.

Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing

Abstract: This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusion processes with killing on $[0,\infty)$. We obtain criteria for the exponential convergence to a unique quasi-stationary distribution in total variation, uniformly with respect to the initial distribution. Our approach is based on probabilistic and coupling methods, contrary to the classical approach based on spectral theory results. Our general criteria apply in the case where $\infty$ is entrance and 0 either regular or exit, and are proved to be satisfied under several explicit assumptions expressed only in terms of the speed and killing measures. We also obtain exponential ergodicity results on the $Q$-process. We provide several examples and extensions, including diffusions with singular speed and killing measures, general models of population dynamics, drifted Brownian motions and some one-dimensional processes with jumps.

On multiplication in $q$-Wiener chaoses

Abstract: We pursue the investigations initiated by Donati-Martin [9] and Effros-Popa [10] regarding the multiplication issue in the chaoses generated by the $q$-Brownian motion ($q\in (-1,1)$), along two directions: $(i)$ We provide a fully-stochastic approach to the problem and thus make a clear link with the standard Brownian setting; $(ii)$ We elaborate on the situation where the kernels are given by symmetric functions, with application to the study of the $q$-Brownian martingales.

The revisited knockoffs method for variable selection in L 1 -penalized regressions

Abstract: We consider the problem of variable selection in regression models. In particular, we are interested in selecting explanatory covariates linked with the response variable and we want to determine which covariates are relevant, that is which covariates are involved in the model. In this framework, we deal with L 1-penalized regression models. To handle the choice of the penalty parameter to perform variable selection, we develop a new method based on the knockoffs idea. This revisited knockoffs method is general, suitable for a wide range of regressions with various types of response variables. Besides, it also works when the number of observations is smaller than the number of covariates and gives an order of importance of the covariates. Finally, we provide many experimental results to corroborate our method and compare it with other variable selection methods.