Convergence de modèles moléculaires vers des modèles de mécanique des milieux continus

The work we present here is focused on the justification of continuum mechanics as a natural asymptotic of molecular theories when the interatomic distance goes to zero. We give a sound theoretical ground to existing models, and derive and next study (apparently) new ones.     

Sur l'existence et l'unicité de solutions de modèles linéaires en aéroacoustique

An aeroacoustic modelling is considered in this Note. A steady flow modifies the classical wave propagations. But using physical assumptions on the data, it is proved an existence and uniqueness result. Furthermore, practical examples prove that one cannot get rid of the required hypothesis.     

Théorème de Poincaré–Alexander pour les domaines modèles

The Poincaré–Alexander Theorem states that holomorphic mappings defined on an open subset of the unit ball of ${\mathbb{C}}^n$ may, under certain conditions, be extended to a biholomorphism of the unit ball. In a complex manifold, every strongly pseudoconvex homogeneous domain is biholomorphic to the unit ball. In an almost complex manifold, the unit ball is not the only strongly pseudoconvex homogeneous domain. A strongly pseudoconvex homogeneous domain is biholomorphic to a model domain. The aim of this paper is to extend this theorem to model domains.     

Points entiers et modèles des courbes algébriques

LetC: F(X, Y)=0 be an algebraic curve of genus 1, over a number fieldK. In this work we construct a modelG(Z,W)=0 of the curveC, over a fixed number fieldL with , having the following property: ifx, y are algebraic integers ofK withF(x, y)=0, thenz=Z(x, y), w=W(x, y) are algebraic integers ofL withG(z, w)=0. Also, the total degree and the height of the polynomialG are bounded. As an application of this result, we give a reduction of the problem to determine effectively the integer points on a curve of genus 2, over a number field, to the problem to determine effectively the integer solutions of an equation of degree 4, over a number field. Also we consider a family of curvesF(X, Y)=0, defined over a number fieldK, which are cyclic coverings ofP ¹ and we calculate, using our previous results, an explicit upper bound for the height of the integer points ofF(X, Y)=0 overK.

     

Principes de déviations modérées pour des modèles autorégressifs d'ordre p

We establish Moderate deviations principles (MDP) for some stable autoregressive models of order p: first for continuous unbounded additive functionnals of this process, second for the estimation error of the regression function (least-squares estimator in the stable linear case, kernel estimator in the Lipschitz non-linear case).     

Estimation des ordres de modèles ARMA faibles multivariés

In this Note, we consider the problem of order selection of vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated, but not necessarily independent. These models are called weak VARMA by opposition to the standard VARMA models, also called strong VARMA models, in which the error terms are supposed to be iid. This selection is based on minimizing an information criterion, especially that introduced by Akaike. The theoretical foundations of the Akaike information criterion (AIC) are not more established when the iid assumption on the noise is relaxed. We propose a modified AIC criterion, and which may be very different from the standard AIC criterion.     

Tests portmanteau multivariés d'adéquation de modèles VARMA faibles

In this Note, we consider portmanteau tests for testing the adequacy of vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent. We relax the standard independence assumption to extend the range of application of the VARMA models, allowing us to treat linear representations of general nonlinear processes. We first study the joint distribution of the quasi-maximum likelihood estimator (QMLE) and the noise empirical autocovariances. We thus obtain the asymptotic distribution of residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We deduce the asymptotic distribution of the Ljung–Box (or Box–Pierce) portmanteau statistics for VARMA models with nonindependent innovations. We propose a method to adjust the critical values of the portmanteau tests.     

Estimation de la précision asymptotique dans l'estimation de modèles ARMA faibles

An estimator of the asymptotic covariance matrix of the least squares estimator of ARMA models is proposed. To deal with the ARMA representations of nonlinear processes, the standard strong assumptions on the noise are replaced by a mixing condition on the observed process. The weak consistency of the proposed estimator is proved.     

Modélisation d'un problème de diffusion avec pyrolyse et ablation

We discuss existence and uniqueness for the solutions of an unusual parabolic quasilinear problem, coming from a heat conduction model problem (atmosphere re-entry of a body) with pyrolysis and weak ablation.     

Modèles de verre de spins à champ moyen et à interactions multiples : résultats rigoureux à basse température

We study the Ising case of the p-spin interaction mean field model for spin glasses. For large p, below the critical temperature, the configuration space naturally decomposes in a sequence of “states”. In the thermodynamic limit, the overlaps between two generic elements of any two different “states” are zero.We also construct systems that provably exhibit several phase transitions between what one might in replica theory call different levels of symmetry breaking.     

Inférence fondée sur la vraisemblance pour des modèles de records

In a time series $\{X_t,t\ge 1\}$, $X_j$ is said to be an upper record if $X_j>\max ?\{X_1,\dots ,X_{j?1}\}$. Some popular models for records are the Yang–Nevzorov and the Linear Drift models. In this note, we introduce for these models the joint likelihood of the record sequence and the indicators of their occurrence. This likelihood can then be used to obtain estimators of the unknown parameters in the models. It can also be used to derive inferential procedures associated with the selection of a proper model for such data.     

Sur l'estimation des modèles autorégressifs d'ordre multiple de séries temporelles

In this Note, we determine the minimum Hellinger distance estimate of a multiple order autoregressive time series model. Under some assumptions which ensure some probabilistic properties, and under other mild conditions, we establish the asymptotic properties of this estimate. As an example, we consider the exponential autoregressive models.