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Displaying similar documents to “On convergence of the empirical mean method for non-identically distributed random vectors”

Empirical estimates in stochastic optimization via distribution tails

Vlasta Kaňková (2010)

Kybernetika

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“Classical” optimization problems depending on a probability measure belong mostly to nonlinear deterministic optimization problems that are, from the numerical point of view, relatively complicated. On the other hand, these problems fulfil very often assumptions giving a possibility to replace the “underlying” probability measure by an empirical one to obtain “good” empirical estimates of the optimal value and the optimal solution. Convergence rate of these estimates have been studied...

On continuous convergence and epi-convergence of random functions. Part II: Sufficient conditions and applications

Silvia Vogel, Petr Lachout (2003)

Kybernetika

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Part II of the paper aims at providing conditions which may serve as a bridge between existing stability assertions and asymptotic results in probability theory and statistics. Special emphasis is put on functions that are expectations with respect to random probability measures. Discontinuous integrands are also taken into account. The results are illustrated applying them to functions that represent probabilities.

Large deviations, central limit theorems and L convergence for Young measures and stochastic homogenizations

Julien Michel, Didier Piau (2010)

ESAIM: Probability and Statistics

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We study the stochastic homogenization processes considered by Baldi (1988) and by Facchinetti and Russo (1983). We precise the speed of convergence towards the homogenized state by proving the following results: (i) a large deviations principle holds for the Young measures; if the Young measures are evaluated on a given function, then (ii) the speed of convergence is bounded in every L norm by an explicit rate and (iii) central limit theorems hold. In dimension 1, we apply these...

On the convergence of the stochastic Galerkin method for random elliptic partial differential equations

Antje Mugler, Hans-Jörg Starkloff (2013)

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

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In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity...

Negative dependence structures through stochastic ordering.

Abdul-Hadi N. Ahmed (1990)

Trabajos de Estadística

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Several new multivariate negative dependence concepts such as negative upper orthant dependent in sequence, negatively associated in sequence, right tail negatively decreasing in sequence and upper (lower) negatively decreasing in sequence through stochastic ordering are introduced. These concepts conform with the basic idea that if a set of random variables is split into two sets, then one is increasing whenever the other is decreasing. Our concepts are easily verifiable and enjoy many...

Thin and heavy tails in stochastic programming

Vlasta Kaňková, Michal Houda (2015)

Kybernetika

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Optimization problems depending on a probability measure correspond to many applications. These problems can be static (single-stage), dynamic with finite (multi-stage) or infinite horizon, single- or multi-objective. It is necessary to have complete knowledge of the “underlying” probability measure if we are to solve the above-mentioned problems with precision. However this assumption is very rarely fulfilled (in applications) and consequently, problems have to be solved mostly on the...

On the convergence of moments in the CLT for triangular arrays with an application to random polynomials

Christophe Cuny, Michel Weber (2006)

Colloquium Mathematicae

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We give a proof of convergence of moments in the Central Limit Theorem (under the Lyapunov-Lindeberg condition) for triangular arrays, yielding a new estimate of the speed of convergence expressed in terms of νth moments. We also give an application to the convergence in the mean of the pth moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.