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.     

Processus d'Antoniadis-Carmona et le principe de déviations modérées

We prove that the uniform moderate deviations principle is satisfied by the empirical measures associated to the Antoniadis-Carmona processes.     

Quelques modèles asymptotiques pour les poutres purement encastrées

We present several limit models for genuinely clamped elastic beams obtained from linear three-dimensional elasticity using an asymptotic method, and we prove the existence and the uniqueness of the solution for these models. We also obtain convergence to the usual clamped beam model.     

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.     

Martingales et grandes déviations pour les arbres binaires de recherche

We establish almost sure and in mean large deviations theorems for the leaf structure of binary search trees (b.s.t.). To this end, a parameterized family of martingales is introduced. This family also allows us to have asymptotic results on the number of final leaves of a b.s.t.     

Déviations modérées pour la moyennisation d'une EDS avec petite diffusion

We prove in this Note the moderate deviation principle (MDP) for the averaging principle of a stochastic differential equation (SDE) in a fast random environment, modelized by an exponentially ergodic Markov process independent of the Wiener process driving the SDE. The main tools will be the method of Puhalskii for exponential tightness and a MDP for inhomogeneous functionals of Markov processes established in [5].     

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.     

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.     

Principes de grandes déviations pour l’estimateur à noyau de la densité de probabilité

We establish pointwise and uniform large deviations principles for nonparametric kernel density estimators. The estimates are based on sequences of independent and identically distributed real random variables.     

Convergence des méthodes particulaires renormalisées pour les systèmes de Friedrichs

We present a study of the renormalized particle scheme. Renormalization is a tool introduced in order to alleviate the SPH particle methods' lack of consistency. A conservative scheme, the weak renormalized scheme, is derived from the general conservation laws weak formulation. We apply this scheme to Friedrichs systems. The weak renormalized scheme being unstable, we introduce a numerical viscosity before applying an explicit Euler time discretization, and thus construct the numerical scheme whose convergence in $L^2$ norm is studied. To cite this article: N. Lanson, J.-P. Vila, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Grandes déviations pour des formes quadratiques de processus gaussiens localement stationnaires

We establish large deviations principles for quadratic forms - tapered periodograms integrated over frequencies, a pre-periodogram integrated over time and frequencies, likelihood ratio — of Gaussian locally stationary processes as defined bx Dahlhaus ([3], [4]).     

Modèles semi-factoriels et modèles de Néron

Let S be the spectrum of a discrete valuation ring with function field K. Let X be a scheme over S. We will say that X is semi-factorial over S if any invertible sheaf on the generic fiber X _K can be extended to an invertible sheaf on X. Here we show that any proper geometrically normal scheme over K admits a proper, flat, normal and semi-factorial model over S. We also construct some semi-factorial compactifications of regular S-schemes, such as Néron models of abelian varieties. The semi-factoriality property for a scheme X/S corresponds to the Néron property of its Picard functor. In particular, one can recover the Néron model of the Picard variety ${{\rm Pic}_{X_K/K,{\rm red}}^0}$ of X _K from the Picard functor Pic _X/S , as in the known case of curves. This provides some information on the relative algebraic equivalence on the S-scheme X.     

Modèles pour les applications fibrées et les polysystèmes

We introduce a fibered version of the classical ‘horseshoe’ of Smale, that one can use to analyze the dynamical properties of diffeomorphisms with a normally hyperbolic invariant manifold and suitable homoclinic intersections. Our abstract model gives rise to fibered dynamics over the Bernoulli shift and to the more particular case of polysystems that we define here, which can be seen as the simultaneous iteration of several maps on the same space in any prescribed order. To cite this article: J.-P. Marco, C. R. Acad. Sci. Paris, Ser. I 346 (2008).     

Sur les valeurs moyennes des fonctions réelles définies pour toutes les valeurs de la variable

Sans résumé     

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.     

Extension du filtre de Chandrasekhar au cas des modèles espace d'état périodiques

This Note extends the Chandrasekhar-type recursions due to Morf, Sidhu, and Kailath (1974) to the case of periodic time-varying state-space models. We show that the S-lagged increments of the one-step prediction error covariance satisfy certain recursions from which we derive some algorithms for linear least squares estimation for periodic state-space models. The proposed recursions have potential computational advantages over the Kalman Filter and, in particular, the periodic Riccati difference equation. To cite this article: A. Aknouche, F. Hamdi, C. R. Acad. Sci. Paris, Ser. I 346 (2008).