GDT "EDP et Calcul Scientifique" du mardi 12 novembre 2019

Conditions aux limites transparentes pour équations de Green-Naghdi linéarisées

Mardi, 12 novembre 2019 - 11:30 - 12:30

La simulation directe du phénomène de propagation des vagues à l'aide des équations d'Euler ou de Navier-Stokes à surface libre est complexe et coûteuse numériquement. Certains phénomène aux grandes échelles sont bien décrit par des modèles réduits plus simples à simuler numériquement; toutefois, ces modèles nécessitent des techniques plus avancées pour imposer les conditions aux limites.

Atelier des doctorants du Mardi 22/10/2019

Quasilinear Elliptic Problems in a Domain with Imperfect Interface and $L^1$ data

Mardi, 22 octobre 2019 - 14:00 - 15:00
The aim of this talk is to present the existence results for a class of quasilinear elliptic problems in a two-component domain and $L^1$ data. I will first give the necessary definitions and assumptions, including the definition of a renormalized solution. I will then discuss the sketch of the proof of the existence of a renormalized solution.
Our main goal is to perform the homogenization process to this class of equations, so I will also present a very brief introduction to the theory of homogenization.

Reliable detection of abrupt changes and a multi-parameter exponential distribution

Jeudi, 21 novembre 2019 - 10:15 - 11:15

The goal of this presentation is to discuss the reliable sequential detection of transient changes in a multi-parameter exponential distribution. The sequentially observed data are represented by a sequence of independent random vectors with the exponentially distributed components.

LAMN property for the drift parameter of diffusion processes from discrete observations

Jeudi, 24 octobre 2019 - 10:15 - 11:15

We first consider a multidimensional diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a Lévy process without Gaussian component, whose drift coefficient depends on a multidimensional unknown parameter. We prove the local asymptotic normality (LAN) property from high-frequency discrete observations with increasing observation window by assuming some hypotheses on the coefficients of the equation, the ergodicity of the solution and the integrability of the Lévy measure.


Spectral disjointness of powers of Interval Exchange Transformations

Lundi, 7 octobre 2019 - 11:00 - 12:00

Firstly, I will present the definition of spectral disjointness of two automorphisms and show a criterion which can be used  to distinguish this property. Secondly, I will show how to see that powers of a generic interval exchange transformation of three intervals satisfy the asumptions of the criterion.

The result is based on a joint work with Adam Kanigowski.


Loi des logarithmes itérés bornée pour des martingales multi-dimensionnelles

Lundi, 30 septembre 2019 - 11:00 - 12:00

Nous allons donner des conditions suffisantes pour la loi des logarithmes itérés bornée
pour des champs aléatoires, en considérant la sommation sur des rectangles. Nous nous concentrons sur
deux classes de champs aléatoires strictement stationnaires : les martingales pour l'ordre lexicographique
et les orthomartingales.

Parameter estimation for a discretely observed non-smooth threshold diffusion model

Jeudi, 12 septembre 2019 - 14:00 - 15:00

Threshold diffusions are regime-switching continuous-time models where the model switches between two or more different model behaviors as the state variable cross certain domains.  We consider the statistical estimation on the switching threshold value for a discretely observed one-dimensional diffusion process.


Invariant measures, matching and the frequency of 0 for signed binary expansions

Lundi, 1 juillet 2019 - 11:00 - 12:00

We introduce a parametrised family of maps $\{S_{\eta}\}_{\eta \in [1,2]}$, called symmetric doubling maps, defined on $[-1,1]$ by $S_\eta (x)=2x-d\eta$, where $d\in \{-1,0,1 \}$. Each map $S_\eta$ generates binary expansions with digits $-1$, 0 and 1. We study the frequency of the digit 0 in typical expansions as a function of the parameter $\eta$. The transformations $S_\eta$ have a natural ergodic invariant measure $\mu_\eta$ that is absolutely continuous with respect to Lebesgue measure.