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Author: Houdré, Christian × search.filters.applied.f.isOrgUnitOfPublicationTitle: College of Sciences ×

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Now showing 1 - 10 of 11
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Topics in sequence comparison and discrete structures

2011-05-11 , Houdré, Christian , Matzinger, Heinrich

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Exponential Inequalities for U-Statistics of Order Two with Constants

2002-12-13 , Houdré, Christian , Reynaud-Bouret, Patricia

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A Characterization of Gaussian Measures via the Isoperimetric Property of Half-Spaces

1995-07-25 , Bobkov, S. G. , Houdré, Christian

If the half-spaces of the form {x\in R^n: x_1 \le c} are extremal in the isoperimetric problem for the product measure \mu^n, n\ge 2, then \mu is Gaussian.

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Variance of Lipschitz Functions and an Isoperimetric Problem for a Class of Product Measures

1995-07-10 , Bobkov, S. G. , Houdré, Christian

The maximal variance of Lipschitz functions (with respect to the \ell_1-distance) of independent random vectors is found. This is then used to solve the isoperimetric problem, uniformly in the class of product probability measures with given variance.

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Converse Poincaré Type Inequalities for Convex Functions

2009-12-07 , Bobkov, S. G. , Houdré, Christian

Converse Poincaré type inequalities are obtained within the class of smooth convex functions. This is, in particular, applied to the double exponential distribution.

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Sharp Constants in Some Multiplicative Sobolev Inequalities

1995-09-16 , Bobkov, S. G. , Houdré, Christian

The optimal constants in the multiplicative Sobolev inequalities where the gradient is estimated in the L_1-norm and the function in two different Lebesgue norms are found. With the optimal constants, these inequalities turn out to still be equivalent to the isoperimetric property of the balls in the Euclidean space. In the course of the proof, relations between Lorentz and Lebesgue spaces are studied (and also applied to some different measures, e.g., Riesz potentials).

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Isoperimetric Constants for Product Probability Measures

1995-07-24 , Bobkov, S. G. , Houdré, Christian

A dimension free lower bound is found for isoperimetric constants of product probability measures. From this, some analytic inequalities are derived.

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Nonparametric estimation for Levy processes with a view towards mathematical finance

2004-11 , Figueroa-Lopez, Enrique , Houdré, Christian

Nonparametric methods for the estimation of the Levy density of a Levy process X are developed. Estimators that can be written in terms of the "jumps" of X are introduced, and so are discrete-data based approximations. A model selection approach made up of two steps is investigated. The first step consists in the selection of a good estimator from a linear model of proposed Levy densities, while the second is a data-driven selection of a linear model among a given collection of linear models. By providing lower bounds for the minimax risk of estimation over Besov Levy densities, our estimators are shown to achieve the "best" rate of convergence. A numerical study for the case of histogram estimators and for variance Gamma processes, models of key importance in risky asset price modeling driven by Levy processes, is presented.

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On the Linear Prediction of Some L^p Random Fields

1995-08 , Cheng, R. , Houdré, Christian

This work is concerned with the prediction problem for a class of L^p-random fields. For this class of fields, we derive prediction error formulas, spectral factorizations, and orthogonal decompositions.

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Dimension Free Weak Concentration of Measure Phenomenon

1995-07-24 , Bobkov, S. G. , Houdré, Christian

For product probability measures \mu^n, we obtain necessary and sufficient conditions (in terms of \mu) for dimension free isoperimetric inequalities of the form \mu^n (A + h[-1,1]^n)\ge R_h(\mu^n(A)) to hold; for a function R such that R(p) > p, for all (some) p \in (0,1), and for h > 0 large enough. Some questions related to the concentration of measure phenomenon are also discussed.

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