Diviseurs Des Nombres Ellipséphiques

Les propriétés multiplicatives des nombres ellipséphiques peuvent être obtenues à l’aide des moments de la série génératrice de cette suite. Nous donnons des estimations précises pour les grands moments par deux méthodes distinctes: l’une combinatoire fournit un résultat précis dans le cas réputé le plus difficile des nombres n’utilisant que les 0 et les 1; la seconde purement analytique fournit un résultat sans condition sur les chiffres.

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On the global central limit theorem for ϕ-mixing random variables

The estimate of the remainder term is obtained in the global central limit theorem for π-mixing r.v.s. As a consequence of Theorem 1 the convergence rate of absolute moments for sums of π-mixing r.v.s. to corresponding absolute moments of the normal r.v. is found. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 2, pp. 233–247, April–June, 1995.     

Equations différentielles linéaires,pour des fonctions d’ensemble

Résumée On étudie l’équation(1), où ϕ est une fonction additive d’ensemble, définie sur une σ-algèbre &, E_P un élément de &, associé au point P, et f une fonction continue de n+1 variables, lipschitzienne par rapport à la dernière. En particulier, on donne une expression simple à l’integrale de l’équation linéaire (5) et du système(22).     

Čebyšev-Grüss-type inequalities revisited

We generalize and improve several inequalities of the ?eby?ev-Grüss-type using least concave majorants of the moduli of continuity of the functions involved. Our focus is on normalized positive linear functionals. We discuss a problem posed by the two Gavreas and also give the solution of a stronger one. In a section about the non-multiplicativity of positive linear operators it is demonstrated that the previous use of second moments is not quite the right choice. This is documented in the case of the classical Hermite-Fejér and de La Vallée Poussin convolution operators.     

Problème des Moments

Abstract. On se propose dans ce papier de donner une caractérisation des fonctions moments définies sur un * -semigroupe qui n'est pas forcément de type fini. Il s'agit en fait d'une généralisation du résultat de Putinar et de Vasilescu donnant une solution du problème des moments dans R ⁿ . On donnera alors en application de ce résultat une caractérisation des suites indéfinies ayant une singularité au point ξ=(1,. . ., 1)∈ C ^p d'ordre au moins 2κ .     

Grüss-type and Ostrowski-type inequalities in approximation theory

We discuss the Grüss inequalities on spaces of continuous functions defined on a compact metric space. Using the least concave majorant of the modulus of continuity, we obtain the Grüss inequality for the functional L(f) = H(f; x), where H:C[a, b] → C[a, b] is a positive linear operator and x ∈ [a, b] is fixed. We apply this inequality in the case of known operators, e.g., the Bernstein operator, the Hermite–Fejér interpolation operator, and convolution-type operators. Moreover, we deduce Grüss-type inequalities using the Cauchy mean-value theorem, thus generalizing results of Chebyshev and Ostrowski. The Grüss inequality on a compact metric space for more than two functions is given, and an analogous Ostrowski-type inequality is obtained. The latter, in turn, leads to one further version of the Grüss inequality. In the appendix, we prove a new result concerning the absolute first-order moments of the classic Hermite–Fejér operator.     

Représentations semi-stables et modules fortement divisibles

Sans résumé Oblatum 1-IV-1998 &9-VI-1998 / Published online: 14 January 1999     

A Smooth Approach to Malliavin Calculus for Lévy Processes

An approach to Malliavin calculus for Lévy processes, discrete in time and smooth in chance, is presented. Each Lévy triple can be satisfied by a Lévy process living on a fixed sample space Ω, which is, in a certain sense, a finite dimensional Euclidean space. The probability measures on Ω characterize the Lévy processes. We compare these measures with the associated Lévy measures, and present several examples. Using chaos expansions for Lévy functionals, even for those having no moments, we can represent all these functionals by polynomials in several variables. There exists an effective method to compute the kernels of the chaos decomposition. Finally, we point out several applications, which are postponed to a succession of papers. Dedicated to Helmut Schwichtenberg.     

On super continuous multifunctions

We define upper (lower) super continuous multifunctions and obtain some characterizations and basic properties of such a multifunction. Also some relationships between the concept of super continuity and known concepts of continuity and strongly Θ-continuity are given. This revised version was published online in June 2006 with corrections to the Cover Date.     

A combinatorial method for calculating the moments of Lévy area

We present a new way to compute the moments of the Lévy area of a two-dimensional Brownian motion. Our approach uses iterated integrals and combinatorial arguments involving the shuffle product.

     

Regularity of Ornstein–Uhlenbeck Processes Driven by a Lévy White Noise

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by Lévy white noise “obtained by subordination of a Gaussian white noise”. Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general cádlág modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.     

Symmetric power functoriality for holomorphic modular forms

Publications mathématiques de l'IHÉS - We show that stationary characters on irreducible lattices $\Gamma < G$ of higher-rank connected semisimple Lie groups are conjugation...     

Wiener Type Regularity of a Boundary Point for the 3D Lamé System

In this paper, we study the 3D Lamé system and establish its weighted positive definiteness for a certain range of elastic constants. By modifying the general theory developed in Maz’ya (J Duke Math 115(3): 479–512, 2002), we then show, under the assumption of weighted positive definiteness, that the divergence of the classical Wiener integral for a boundary point guarantees the continuity of solutions to the Lamé system at this point.     

Functional Limit Theorems for Multiparameter Fractional Brownian Motion

We prove a general functional limit theorem for multiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional Lévy’s modulus of continuity and many other results are its particular cases. Applications to approximation theory are discussed.      

Heavy traffic approximation for the stationary distribution of stochastic fluid networks

It has recently been shown that in the heavy traffic limit, the stationary distribution of the scaled queue length process of a Generalized Jackson Network converges to the stationary distribution of its corresponding Reflected Brownian Motion limit. In this paper, we show that this “interchange of limits” is valid for Stochastic Fluid Networks with Lévy inputs. Furthermore, under additional assumptions, we extend the result to show that the interchange is valid for moments of the stationary distribution and for state-dependent routing. The results are obtained using monotonicity and sample-path arguments.     

Banach–Zaretsky theorem for compactly absolutely continuous mappings

For mappings of an interval into locally convex spaces, convex and compact convex analogs of absolute continuity, bounded variation, and the Luzin N-property are introduced and studied. We prove that, in the general case, a convex analog of the Banach–Zaretsky criteria can be “split” into sufficient and necessary conditions. However, in the Fréchet-space case, we have an exact compact analog of the criteria.     

Monodromy of certain Painlevé–VI transcendents and reflection groups

We study the global analytic properties of the solutions of a particular family of Painlevé VI equations with the parameters β=γ=0, δ= and 2α=(2μ-1)² with arbitrary μ, 2μ≠∈ℤ. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection group. We show that the finite orbits of this action correspond to the algebraic solutions of our Painlevé VI equation and use this result to classify all of them. We prove that the algebraic solutions of our Painlevé VI equation are in one-to-one correspondence with the regular polyhedra or star-polyhedra in the three dimensional space. Oblatum 19-III-1999 & 25-XI-1999?Published online: 21 February 2000     

Gaussian fluctuations for random walks in random mixing environments

We consider a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions. Continuing our previous work [2] for the law of large numbers, we prove here that the fluctuations are Gaussian when the environment is Gibbsian satisfying the “strong mixing condition” of Dobrushin and Shlosman and the mixing rate is large enough to balance moments of some random times depending on the path. Under appropriate assumptions the annealed Central Limit Theorem (CLT) applies in both nonnestling and nestling cases, and trivially in the case of finite-dependent environments with “strong enough bias”. Our proof makes use of the asymptotic regeneration scheme introduced in [2]. When the environment is only weakly mixing, we can only prove that if the fluctuations are diffusive then they are necessarily Gaussian. Partially supported by CNRS, UMR 7599 “Probabilités et Modèles aléatoires”. Partially supported by NSF grant number DMS-0302230.     

On approximating periodic functions by singular integrals with positive kernels

In the two-dimensional case, new approximation characteristics for functions belonging to saturation classes of continuity modules for the spaces L_p of periodic functions are obtained. The problem of approximating a function by an analog of Fejér’s integral in the space of periodic functions square integrable on the period is considered. Bibliography: 5 titles. Dedicated to the 100th anniversary of G. M. Goluzin’s birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 51–72.     

On the dirichlet problem for fully nonlinear parabolic equations

The paper describes a new class of fully nonlinear second-order parabolic equations. The peculiarity of this class in the nonlinear dependence of the equations both on the first-order time derivative and second-order spatial ones. Application of the classical continuity method to solve the first initial-boundary value problem for such equations is also discussed. Bibliography: 15 titles. Published inZapiski Nauchnykh Seminarov POMI, Vol. 233, 1996, pp. 101–111.