# 2 mars 2020: 2 événements

### Lundi 2 mars 09:30-10:30 - Emmanuel Caron - Université Lumière Lyon 2, Laboratoire ERIC EA 3083

Séminaire PS : The regression models with dependent errors

Résumé : We consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan (1973), who proved a Central Limit Theorem for the usual least squares estimator under general conditions on the design and on the error process. Whatever the design satisfying Hannan’s conditions, we define an estimator of the covariance matrix and we prove its consistency under very mild conditions. As an application, we show how to modify the usual tests on the linear model in this dependent context, in such a way that the type-I error rate remains asymptotically correct.
Then, we present some results on the non-parametric regression model in the case where the error process is a Gaussian stationary sequence.

Lieu : Salle 316B - 16 route de gray
25030 Besançon cedex

En savoir plus : Planning des séminaires 2019-2020

### Lundi 2 mars 11:00-12:00 - Salem Samir - Institut de Mathématiques de Toulouse, Université Paul Sabatier

Séminaire PS : Propagation of chaos for the Boltzmann equation with soft potentials

Résumé : This talk deals with the derivation of the space homogeneous Boltzmann equation in dimension 3, from a Kac-like interacting particles system. The collision kernel is of the form $B(z,\cos(\theta))=|z|^\gamma b(\cos(\theta))$ with $\sin(\theta)b(\cos(\theta))\sim \theta^-1-\nu$ for $\gamma\in (-2,0)$ and $\nu\in(0,2)$ satisfying $\gamma+\nu>0$. The result is obtained by a compacity argument, and the convergence result is given without rate, as in the work by Fournier and Hauray concerning the Landau equation.

Lieu : Salle 316B - 16 route de gray
25030 Besançon cedex

En savoir plus : Planning des séminaires 2019-2020