Displaying similar documents to “Strong approximation for set-indexed partial sum processes via KMT constructions III”

On a variant of random homogenization theory: convergence of the residual process and approximation of the homogenized coefficients

Frédéric Legoll, Florian Thomines (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider the variant of stochastic homogenization theory introduced in [X. Blanc, C. Le Bris and P.-L. Lions, 343 (2006) 717–724.; X. Blanc, C. Le Bris and P.-L. Lions, 88 (2007) 34–63.]. The equation under consideration is a standard linear elliptic equation in divergence form, where the highly oscillatory coefficient is the composition of a periodic matrix with a stochastic diffeomorphism. The homogenized limit of this problem has been identified in [X. Blanc, C. Le Bris and P.-L....

A central limit theorem for triangular arrays of weakly dependent random variables, with applications in statistics

Michael H. Neumann (2013)

ESAIM: Probability and Statistics

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We derive a central limit theorem for triangular arrays of possibly nonstationary random variables satisfying a condition of weak dependence in the sense of Doukhan and Louhichi [84 (1999) 313–342]. The proof uses a new variant of the Lindeberg method: the behavior of the partial sums is compared to that of partial sums of Gaussian random variables. We also discuss a few applications in statistics which show that our central limit theorem is tailor-made for statistics of different type. ...

Homogenization of systems with equi-integrable coefficients

Marc Briane, Juan Casado-Díaz (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we prove a H-convergence type result for the homogenization of systems the coefficients of which satisfy a functional ellipticity condition and a strong equi-integrability condition. The equi-integrability assumption allows us to control the fact that the coefficients are not equi-bounded. Since the truncation principle used for scalar equations does not hold for vector-valued systems, we present an alternative approach based on an approximation result by Lipschitz functions...

Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs

Abdellah Chkifa, Albert Cohen, Ronald DeVore, Christoph Schwab (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to...

Simulation and approximation of Lévy-driven stochastic differential equations

Nicolas Fournier (2011)

ESAIM: Probability and Statistics

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We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like ||d near , for some ∈ (1,2), we obtain an error of order 1/√ with a computational cost of order . For a similar error when neglecting...

A generalized mean-reverting equation and applications

Nicolas Marie (2014)

ESAIM: Probability and Statistics

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Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0] (> 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability...

Dimension reduction for −Δ1

Maria Emilia Amendola, Giuliano Gargiulo, Elvira Zappale (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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A 3D-2D dimension reduction for −Δ is obtained. A power law approximation from −Δ as  → 1 in terms of -convergence, duality and asymptotics for least gradient functions has also been provided.

Large deviations for directed percolation on a thin rectangle

Jean-Paul Ibrahim (2011)

ESAIM: Probability and Statistics

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Following the recent investigations of Baik and Suidan in [(2005) 325–337] and Bodineau and Martin in [10 (2005) 105–112 (electronic)], we prove large deviation properties for a last-passage percolation model in ℤ whose paths are close to the axis. The results are mainly obtained when the random weights are Gaussian or have a finite moment-generating function and rely, as in [J. Baik and T.M. Suidan, (2005) 325–337] and [T. Bodineau and J. Martin, 10 (2005) 105–112 (electronic)],...

Fast approximation of minimum multicast congestion – Implementation VERSUS Theory

Andreas Baltz, Anand Srivastav (2010)

RAIRO - Operations Research

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The problem of minimizing the maximum edge congestion in a multicast communication network generalizes the well-known -hard multicommodity flow problem. We give the presently best theoretical approximation results as well as efficient implementations. In particular we show that for a network with edges and multicast requests, an OPT + exp(1)ln)-approximation can be computed in lnln) time, where  bounds the time for computing an -approximate minimum Steiner tree. Moreover, we present...

Euler schemes and half-space approximation for the simulation of diffusion in a domain

Emmanuel Gobet (2010)

ESAIM: Probability and Statistics

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This paper is concerned with the problem of simulation of , the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain : namely, we consider the case where the boundary is killing, or where it is instantaneously reflecting in an oblique direction. Given discretization times equally spaced on the interval , we propose new discretization schemes: they are fully implementable and provide a weak error of order under some...