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Uniform Convergence (uniform + convergence)

Distribution by Scientific Domains
Mathematics and Statistics55%

Selected Abstracts

Optimal Nonparametric Estimation of First-price Auctions

ECONOMETRICA, Issue 3 2000
Emmanuel Guerre
This paper proposes a general approach and a computationally convenient estimation procedure for the structural analysis of auction data. Considering first-price sealed-bid auction models within the independent private value paradigm, we show that the underlying distribution of bidders' private values is identified from observed bids and the number of actual bidders without any parametric assumptions. Using the theory of minimax, we establish the best rate of uniform convergence at which the latent density of private values can be estimated nonparametrically from available data. We then propose a two-step kernel-based estimator that converges at the optimal rate. [source]

On some geometric and topological properties of generalized Orlicz,Lorentz sequence spaces

MATHEMATISCHE NACHRICHTEN, Issue 2 2008
Foralewski
Abstract Generalized Orlicz,Lorentz sequence spaces ,, generated by Musielak-Orlicz functions , satisfying some growth and regularity conditions (see [28] and [33]) are investigated. A regularity condition ,,2 for , is defined in such a way that it guarantees many positive topological and geometric properties of ,,. The problems of the Fatou property, the order continuity and the Kadec,Klee property with respect to the uniform convergence of the space ,, are considered. Moreover, some embeddings between ,, and their two subspaces are established and strict monotonicity as well as lower and upper local uniform monotonicities are characterized. Finally, necessary and sufficient conditions for rotundity of ,,, their subspaces of order continuous elements and finite dimensional subspaces are presented. This paper generalizes the results from [19], [4] and [17]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Proximal and uniform convergence on apartness spaces

MLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 3 2003
Lumini, a Simona Vī
Abstract The main purpose of this paper is to investigate constructively the relationship between proximal convergence, uniform sequential convergence and uniform convergence for sequences of mappings between apartness spaces. It is also shown that if the second space satisfies the Efremovic axiom, then proximal convergence preserves strong continuity. [source]

Multigrid methods for the symmetric interior penalty method on graded meshes

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 6 2009
S. C. Brenner
Abstract The symmetric interior penalty (SIP) method on graded meshes and its fast solution by multigrid methods are studied in this paper. We obtain quasi-optimal error estimates in both the energy norm and the L2 norm for the SIP method, and prove uniform convergence of the W -cycle multigrid algorithm for the resulting discrete problem. The performance of these methods is illustrated by numerical results. Copyright © 2009 John Wiley & Sons, Ltd. [source]

On the maximum principle and its application to diffusion equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2007
T. Stys
Abstract In this article, an analog of the maximum principle has been established for an ordinary differential operator associated with a semi-discrete approximation of parabolic equations. In applications, the maximum principle is used to prove O(h2) and O(h4) uniform convergence of the method of lines for the diffusion Equation (1). The system of ordinary differential equations obtained by the method of lines is solved by an implicit predictor corrector method. The method is tested by examples with the use of the enclosed Mathematica module solveDiffusion. The module solveDiffusion gives the solution by O(h2) uniformly convergent discrete scheme or by O(h4) uniformly convergent discrete scheme. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007 [source]

Trajectory planning for boundary controlled parabolic PDEs with varying parameters defined on a parallelepiped

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009
Thomas Meurer
The trajectory planning and feedforward tracking control problem is considered for a boundary controlled diffusion-reaction system with a spatially and time varying reaction parameter defined on a 3-dimensional parallelepiped. For this, an implicit state and input parametrization in terms of a basic output via a Volterra-type integral equation with operator kernel is determined, which is solved recursively by means of a series ansatz. The absolute and uniform convergence of the resulting series is verified by restricting the reaction parameter and the basic output to a certain but broad Gevrey class. Hence, assigning an admissible desired trajectory for the basic output directly yields the respective feedforward control, which is required to realize a desired spatio-temporal transition path. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Homogenization of Hamilton-Jacobi-Bellman equations with respect to time-space shifts in a stationary ergodic medium

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2008
Elena Kosygina
We consider a family {u, (t, x, ,)}, , < 0, of solutions to the equation ,u,/,t + ,,u,/2 + H (t/,, x/,, ,u,, ,) = 0 with the terminal data u,(T, x, ,) = U(x). Assuming that the dependence of the Hamiltonian H(t, x, p, ,) on time and space is realized through shifts in a stationary ergodic random medium, and that H is convex in p and satisfies certain growth and regularity conditions, we show the almost sure locally uniform convergence, in time and space, of u,(t, x, ,) as , , 0 to the solution u(t, x) of a deterministic averaged equation ,u/,t + H,(,u) = 0, u(T, x) = U(x). The "effective" Hamiltonian H, is given by a variational formula. © 2007 Wiley Periodicals, Inc. [source]

Stochastic homogenization of Hamilton-Jacobi-Bellman equations

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 10 2006
Elena Kosygina
We study the homogenization of some Hamilton-Jacobi-Bellman equations with a vanishing second-order term in a stationary ergodic random medium under the hyperbolic scaling of time and space. Imposing certain convexity, growth, and regularity assumptions on the Hamiltonian, we show the locally uniform convergence of solutions of such equations to the solution of a deterministic "effective" first-order Hamilton-Jacobi equation. The effective Hamiltonian is obtained from the original stochastic Hamiltonian by a minimax formula. Our homogenization results have a large-deviations interpretation for a diffusion in a random environment. © 2005 Wiley Periodicals, Inc. [source]