Sur les natures des processus solutions de certaines equations stochastiques aux differences

A study of the natures of the processes that are solutions of some finite difference stochastic equations, the right‐hand member of which is a stationary process, is given in the paper. Since the principal application of the present work concerns ARIMA models with or without seasonal variation, these processes are named G‐ARIMA. First, a criterion for a G‐ARIMA process to be stationary is established and some properties of a special class of stationary G‐ARIMA processes are studied. Then, we deduce some conditions for a finite difference stochastic equation to uniquely possess non‐stationary solutions. These have the particular property that their backward shift‐operator may be either a linear or a non‐linear operator, depending on the initial conditions of the solutions. So criteria are established for a non‐stationary G‐ARIMA process to have a bounded linear backward shift operator. Finally, some further properties of the G‐ARIMA processes are given, by comparing them with the broad class of V‐bounded processes. This comparison shows that a non‐stationary process cannot be at the same time G‐ARIMA and V‐bounded.     

Presentation geometrique des methodes de calcul des valeurs propres

Summary We present a survey of recent work on the convergence of methods for computing eigenvalues and eigenvectors of matrices. We try to maintain a geometric point of view and give pride of place to the R algorithm.

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Cet article a été ecrit pendant le sejour de l'auteur en laboratoire d'Analyse Numérique de l'Université de Paris 6     

Sur les solutions continues de deux équations fonctionnelles

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Dedié à János Aczél à l'occasion de son 60ème anniversaire     

Sur l'analyticité des solutions de certaines équations aux opérateurs pseudodifférentiels

Sommaire Dans ce travail on obtient un résultat concernant l'analyticité des solutions de certaines équations où interviennent certains opérateurs pseudodifférentiels du type elliptique, tels qu'ils ont été definis dans [1].

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Sunto In questo lavoro si ottiene un risultato concernente l'analiticità delle soluzioni di certe equazioni nelle quali intervengono certi operatori pseudo differenziali di tipo ellittico.

     

Approximations rationnelles des valeurs de la fonction Gamma aux rationnels

As a corollary of a more general result, we present new rational approximations un/vn to the value of the Gamma function at a given rational point, where un and vn are solutions of a linear recurrence of order 3 with polynomials coefficients.     

A propos de l'existence et de la régularité des solutions de certaines inéquations quasi-variationnelles

We prove existence and regularity results for a general inequality including fixed point problems, variational and quasi variational inequalities. Examples of such problems are considered.     

Dimension de l’anneau des polynomes a valeurs entieres

Let A be a commutative domain with quotient field K and A_S the ring of integer-valued polynomials thus A_S={f∈K[X]; f(A)⊂A}; we show that the Krull dimension of A_S is such that dim A_S≥dim A[X]-1 and give examples where dim A_S=dim A[X]-1. Considering chains of primes of A_S above a maximal idealm of finite residue field, we give also examples where the length of such a chain can arbitrarily be prescribed (whereas in A[X] the length of such chains is always 1). To provide such examples we consider a pair of domains A⊂B sharing an ideal I such that A/I is finite; we give sufficient conditients to have A_S⊂B[X] and show that in this case dim A_S=dim B[X]. At last, as a generalisation of Noetherian rings of dimension 1, we consider domains with an ideal I such that A/I is finite and a power Iⁿ of I is contained in a proper principal ideal of A; for such domains we show that every prime of A_S above a primem containing I is maximal.      

Dérivée des petites valeurs propres des surfaces de Riemann

On estime la dérivée des petites valeurs propres du Laplacien sur une famille de surfaces de Riemann. Ces valeurs propres sont considérées comme des fonctions sur l'espace de Teichmüller, et l'estimation des dérivées peut s'exprimer dans ce contexte. Received: December 21, 1995     

Connexite et densite des representations irreductibles des groupes de surface dans le groupe general lineaire

We show that any representation of the fundamental group of an orientable surface Σ in GL_n(R) admits a base of neighborhoods in any of which the subset of irreducible representations is a pathwise connected and dense subset, as long as the genus of Σ is big enough.     

Ramification de certaines extensions de Lie p-adiques

Let G be a p-adic Lie group and let K be a finite extension of the p-adic number field ℚ _p . There are finitely many filtrations of G which could be ramification filtrations of totally ramified Galois extensions of K with Galois group G. Received: 19 October 1998     

Problème de Dirichlet relatif à une perturbation non lineaire des espaces harmoniques

In this paper, we prove for a more general semi-linear perturbation of linear harmonic spaces, the existence and the unicity of the solution of the Dirichlet problem and we apply our results for the non-linear stationary Schrödinger equation.     

Le rang du systeme lineaire des racines d'une algebre de lie rigide resoluble complexe

Adams and Conway have stated without proof a result which says, roughly speaking, that the representation ring R(G) of a compact, connected Lie group G is generated as a λ-ring by elements in 1-to-1 correspondence with the branches of the Dynkin diagram. In this note we present an elementary proof of this.     

Equations fonctionnelles et recherche de sous-groupes

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Dedié à János Aczél à l'occasion de son 60ème anniversaire