Propriétés asymptotiques des processus de branchement en environnement aléatoire

Let (Z_n) be a branching process in a random environment. If the process in sub-critical or critical, we study the convergence rate of the survival probability P(Z_n>0) as n→∞; if the process is supercritical, we give a necessary and sufficient condition for the convergence in L^p of the natural martingale, where p>1 is given.     

Propriétés asymptotiques des M-estimateurs pondérés pour des données clusterisées

We study the class of weighted M-estimators, which is a variant of M-estimators introduced by Huber in 1964 for the study of robustness. We give sufficient conditions to establish the consistency and asymptotic normality of these estimators for clustered data.     

Propriétés probabilistes des processus GARCH périodiques

This Note examines the probabilistic structure of a GARCH-type stochastic difference equation with periodically time-varying parameters. We propose necessary and sufficient conditions ensuring the existence of stationary solutions, geometrically ergodic (in the periodic sense) and having finite higher-order moments. To cite this article: A. Bibi, A. Aknouche, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Propriétés asymptotiques d'un estimateur dans un modèle non linéaire à effets mixtes

We propose an estimator of nonlinear mixed effects model's parameters, obtained by maximization of simulated pseudo likelihood. This simulated criterion is constructed from the likelihood of a Gaussian model whose means and variances are given by Monte Carlo approximations of means and variances of the true model. If the number of experimental units and the sample size of Monte Carlo simulations are respectively-denoted by N and K, we obtain the strong consistency and asymptotic normality of the estimator when N tends to infinity and the ratio √N/K tends to zero.     

Propriétés et applications d'un circuit flipflop ultra-rapide

Sans résumé     

Propriétés spectrales des restrictions d'opérateurs de la classe \mathbb{A}

We discuss here the question whether there exists an invariant subspace for a contraction T in the class such that the spectrum of the restriction of T on is the whole closed unit disc.     

Propriétés de l'EMV de rupture de processus de Poisson

This Note concerns the estimation of the parameter of the intensity of an inhomogeneous spatial Poisson process by the maximum likelihood method. We consider an intensity admitting a discontinuity along a closed curve depending of an unknown parameter. The established results show the consistency, the convergence in law and the convergence of the moments of the maximum likelihood estimator.     

Propriétés de quelques quadratures dédnites de l'intégration des expressions différentielles à deux variables

Sans résumé     

Sur les Propriétés Arithmétiques de la Fonction de Tschakaloff

Let P and Q be non-zero polynomials with integer coefficients; suppose that all the roots of Q are rational numbers, and that Q(n) 0 for every n N. Let q Z, with |q| 2, and let Q^*. We prove that the number is irrational.From this we deduce linear independence results over Q for the values at x = of Tschakaloff's function Ta(x) = , of its derivatives, and of its primitives. The proof uses Loxton and Van der Poorten's extension of Mahler's transcendence method, which leads, in this case, only to irrationality results.     

Propriétés d'indépendance algébrique de valeurs de séries de Hecke–Mahler

Here we characterize in a complete and explicit way the relations of algebraic dependence over $\mathbb{Q}$ of complex values of Hecke–Mahler series at algebraic points of the multiplicative group ${\mathbb{G}}_{\mathrm{m}}^2(\mathbb{C})$. Our result contains previous results of Loxton and van der Poorten, Mahler, and Masser. To cite this article: F. Pellarin, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Sur les sous-variétés des tores

In Invent. Math. 126 (2000), pp. 513–545, we gave a proof of Lang's conjecture on Abelian varieties leading to an effective bound for the number of translates involved. We show here that the method can be extended to give a similar statement for the Mordell–Lang plus Bogomolov theorem proven by B. Poonen and independently by S. Zhang. We deal in detail with tori for which effective results have been obtained by J.-H. Evertse and H. P. Schlickewei; we improve on these mainly by providing polynomial bounds in the degree instead of doubly exponential ones. We also state a theorem for Abelian varieties. In both cases the strategy of proof is based on the approach of Mumford and Vojta–Faltings–Bombieri together with an effective Bogomolov property and therefore does not rely on either equidistribution nor subspace theorem arguments.     

Etudes des propriétés de situation des surfaces cubiques

Sans résuméDie diesen Aufsatz begleitende Figur findet man am Ende des Aufsatzes.