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Featured researches published by Hacène Djellout.


Annals of Probability | 2004

Transportation cost-information inequalities and applications to random dynamical systems and diffusions

Hacène Djellout; Arnaud Guillin

We first give a characterization of the L1-transportation cost-information inequality on a metric space and next find some appropriate sufficient condition to transportation cost-information inequalities for dependent sequences. Applications to random dynamical systems and diffusions are studied.


Stochastic Processes and their Applications | 2001

Moderate deviations for Markov chains with atom

Hacène Djellout; Arnaud Guillin

We obtain in this paper moderate deviations for functional empirical processes of general state space valued Markov chains with atom under weak conditions: a tail condition on the first time of return to the atom, and usual conditions on the class of functions. Our proofs rely on the regeneration method and sharp conditions issued of moderate deviations of independent random variables. We prove our result in the nonseparable case for additive and unbounded functionals of Markov chains, extending the work of de Acosta and Chen (J. Theoret. Probab. (1998) 75-110) and Wu (Ann. Probab. (1995) 420-445). One may regard it as the analog for the Markov chains of the beautiful characterization of moderate deviations for i.i.d. case of Ledoux 1992. Some applications to Markov chains with a countable state space are considered.


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2011

Lipschitzian norm estimate of one-dimensional Poisson equations and applications

Hacène Djellout

By direct calculus we identify explicitly the Lipschitzian norm of the solution of the Poisson equation −LG = g in terms of various norms of g, where L is a Sturm–Liouville operator or generator of a non-singular diffusion in an interval. This allows us to obtain the best constant in the L1-Poincare inequality (a little stronger than the Cheeger isoperimetric inequality) and some sharp transportation–information inequalities and concentration inequalities for empirical means. We conclude with several illustrative examples. Resume. Par un calcul direct, on identifie explicitement la norme Lipschitzienne de la solution de l’equation de Poisson −LG= g en terme de differentes normes de g, ou L est l’operateur de Sturm–Liouville ou le generateur d’une diffusion non singuliere sur un intervalle. Ainsi, nous pouvons obtenir, d’une part la meilleure constante dans l’inegalite de Poincare L1 (une inegalite un peu plus forte que l’inegalite isoperimetrique de Cheeger) et d’autre part certaines inegalites de transport-information et de concentration fines pour la moyenne empirique. On conclut avec des exemples illustratifs. MSC: 47B38; 60E15; 60J60; 34L15; 35P15


Statistical Inference for Stochastic Processes | 1999

Large and Moderate Deviations for Estimators of Quadratic Variational Processes of Diffusions

Hacène Djellout; Arnaud Guillin

AbstractFor a diffusion process dXt = σdBt + b(t, Xt)dt with (σt) unknown, we study the large and moderate deviations of the estimator


Annals of Applied Probability | 2014

Deviation inequalities, moderate deviations and some limit theorems for bifurcating Markov chains with application

S. Valère Bitseki Penda; Hacène Djellout; Arnaud Guillin


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2014

Deviation inequalities and moderate deviations for estimators of parameters in bifurcating autoregressive models

S. Valère Bitseki Penda; Hacène Djellout

\bar \Theta _n (t): = \sum\nolimits_{k = 0}^{\left[ {nt} \right]} {(X_{k/n} - X_{(k - 1)/n} )^2 }


Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2006

Moderate deviations of empirical periodogram and non-linear functionals of moving average processes

Hacène Djellout; Arnaud Guillin


Stochastics and Stochastics Reports | 2002

Moderate deviations for martingale differences and applications to φ -mixing sequences

Hacène Djellout

of the quadratic variational process


Esaim: Probability and Statistics | 2014

MODERATE DEVIATIONS FOR THE DURBIN-WATSON STATISTIC RELATED TO THE FIRST-ORDER AUTOREGRESSIVE PROCESS

S. Valère Bitseki Penda; Hacène Djellout; Frédéric Proïa


Statistics & Probability Letters | 2014

Large and moderate deviations of realized covolatility

Hacène Djellout; Yacouba Samoura

\Theta (t) = \int_0^t {\sigma _s^2 {\text{d}}} s

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Arnaud Guillin

Blaise Pascal University

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Hui Jiang

Nanjing University of Aeronautics and Astronautics

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Laure Dumaz

École Normale Supérieure

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