Régularité de la loi du maximum de processus gaussiens réguliers

Let X be a real-valued Gaussian process with a one-dimensional parameter. If the sample paths of X are of class C^2k, k integer and if the marginal distributions of X and its derivatives have no degeneracy, then the distribution function of the maximum on a bounded interval is of class C^k. We give a recurrence method allowing to express the derivatives by means of certain implicit formulae.     

Sur la convergence de certaines intégrales de la théorie du potentiel

Sans résuméEn hommage au professeurOstrowski     

Une variante à la Coxeter du groupe de Steinberg

LetG _n ()be the semi-direct product of the symmetric groupS _n by the Steinberg groupSt _n ()of a ringWe first prove thatG _n ()has a Coxeter-type presentation. The canonical morphism St _n () GL _n ()extends to a group homo G_n() GL _n ()We next determine the kernel of for n = We also give an expression for the generator of the algebraic K group K ₂(Z)of the integers in terms of permutation matrices.     

Une caracterisation du type de la loi de Cauchy-conforme sur ℝ n

Résumé La loi de Cauchy-conforme est la mesure de probabilité sur ⁿ de densitéC/(1+X²)ⁿ. Le type d'une mesure sur ⁿ étant l'ensemble des mesures images de par les similitudes-translations de ⁿ et étant une mesure de probabilité sans atome, on démontre que le type de est invariant par les inversions de ⁿ si et seulement si est du type de la loi de Cauchy-conforme.

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The conformal Cauchy law is the probability on ⁿ with densityC/(1+X²)ⁿ. It is shown that for a non-atomic measure on ⁿ the following is true: its type is invariant under inversions of ⁿ if and only if it is the type of a conformal Cauchy law. (The type of a measure is defined as the set of its images under similarities and translations.)

     

Vitesse de convergence presque sûre de l'estimateur à noyau du maximum de vraisemblance local

We consider the local maximum likelihood estimation of $\theta (x)$, unknown parameter of the conditional distribution of Y given $X=x$. The aim of this Note is the study of strong uniform consistency rates of the local maximum likelihood kernel estimator. Under suitable regularity conditions, we establish a uniform law of the logarithm for the maximal deviation of this estimator. The method of proof is based upon functional limit laws derived by modern empirical process theory. To cite this article: D. Blondin, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Décroissance non exponentielle du noyau de la chaleur

Summary In this paper, we give estimates on the heat kernel on the diagonal in terms of exp[–|Logt|], >1 when1 vanishes. Moreover, we compute, by means of the stochastic calculus of variations, the decay of the flatness of some heat kernels. On the other hand, we show that the computations in both cases are very similar.     

Sur la monodromie du problème de Cauchy ramifié

In this paper, we study the monodromy of the ramified Cauchy problem for operators with multiple characteristics of constant multiplicity. More precisely, we give an estimation of the eigenvalues of the solution's monodromy, first with the assumptions of the theorem of Hamada–Leray–Wagschal, then with the assumptions of the theorem of Leichtnam.     

Équations du filtrage non linéaire de la prédiction et du lissage

We establish equations of non linear filtering, prediction (extrapolation) and smoothing (interpolation) in the case where the signal is a non degenerate diffusion process, and the observation is a noisy functional of the signal. We consider both the case of observation noise correlated with the signal, and the opposite case where we establish “robust” form of the equations. We study finally the case of unbounded coefficients, and the case where there is a feedback from the observation to the signal.     

Estimations du Noyau de la Chaleur sur les Espaces Homogènes

We give upper and lower gaussian estimates for the heat kernel for canonical sub-laplacians on homogeneous spaces of Lie groups. We prove that homogeneous spaces of Lie groups of polynomial growth have the doubling property. We deduce Poincaré inequalities on these spaces.

     

Quelques remarques concernant la mesure du «rise time» de photomultiplicateurs

Sans résumé     

Groupes résolubles de difféomorphismes de l’intervalle,du cercle et de la droite

We give a complete classification (from the algebraic and dynamical points of view) of solvable groups of orientation preserving C²-diffeomorphisms of the interval, the circle and the real line. We also give some complementary results in the real-analytic case.     

Singularités rationnelles du modèle entier d'un affinoïde de la droite projective

We consider an affinoid of the projective line over a complete discrete valuation field. We show that its affine normal model over the ring of integers has only rational singularities.     

Estimation de la matrice de variance asymptotique des estimateurs du QMV de modèles ARMA faibles multivariés

In this Note, we consider the problems of estimating the asymptotic variance of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak VARMA). We first give expressions for the derivatives of the VARMA residuals in terms of the parameters of the models. Secondly we give an explicit expression of the asymptotic variance of the QMLE, in terms of the VAR and MA polynomials, and of the second- and fourth-order structure of the noise. We deduce a consistent estimator of the asymptotic variance of the QMLE.     

Analyticité globale de la solution du problème ∂¯-Neumann pour une classe de domaines de ℂn

Let Ω be a bounded, regular and pseudoconvex domain in ℂⁿ, Ω, where ρ is plurisubharmonic and real analytic on ℂ^{n − 1}_z. Then, if we suppose that ρ is strictly plurisubharmonic on ρ = 0, we have the global real analytic regularity of the ∂¯-Neumann problem on Ω for the (0, q)-forms.     

Sur les égalités du miroir et certaines formes faibles de la conjecture de Greenberg

Let p be an odd prime. For any CM number field K containing a primitive p^th-root of unity, class field theory and Kummer theory put together yield the well known reflection inequality ^+– between the plus and minus parts of the -invariant of K. Greenbergs conjecture asserts that ⁺ is always trivial. We study here a weak form of this conjecture, namely ⁺=^– if and only if ⁺=^–=0.     

Prescription de la courbure de Ricci au voisinage de la métrique hyperbolique

On the unit ball of, one considers the standard hyperbolic metric H₀ whose Ricci curvature equals R₀ and Riemann-Christoffel curvature is. We prove that, for any symmetric tensor R near R₀, there exists a unique metric H near H₀ whose Ricci curvature is R. We deduce in the C^∞ case that the image of the Riemann-Christoffel operator is a submanifold in a neighborhood of. Finally, we study more precisely the Ricci equation in dimension 2.