Hacène Djellout
Blaise Pascal University
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Featured researches published by Hacène Djellout.
Annals of Probability | 2004
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
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
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
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
S. Valère Bitseki Penda; Hacène Djellout; Arnaud Guillin
Annales De L Institut Henri Poincare-probabilites Et Statistiques | 2014
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
Hacène Djellout; Arnaud Guillin
Stochastics and Stochastics Reports | 2002
Hacène Djellout
of the quadratic variational process
Esaim: Probability and Statistics | 2014
S. Valère Bitseki Penda; Hacène Djellout; Frédéric Proïa
Statistics & Probability Letters | 2014
Hacène Djellout; Yacouba Samoura
\Theta (t) = \int_0^t {\sigma _s^2 {\text{d}}} s