WorldCat Identities

Bakry, D. (Dominique)

Overview
Works: 47 works in 127 publications in 4 languages and 1,264 library holdings
Genres: Conference papers and proceedings 
Roles: Author, Contributor, Thesis advisor, Editor, Other, htt, xxx
Classifications: QA3, 519.2
Publication Timeline
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Most widely held works by D Bakry
Analysis and geometry of Markov diffusion operators by D Bakry( )

12 editions published between 2013 and 2016 in English and held by 538 WorldCat member libraries worldwide

"The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic"--Back cover
Lectures on probability theory : Ecole d'été de probabilités de Saint-Flour XXII, 1992 by D Bakry( )

26 editions published between 1994 and 2008 in 3 languages and held by 455 WorldCat member libraries worldwide

Annotation
Current trends in potential theory : conference proceedings, Bucharest (Romania), September 2002 and 2003( Book )

7 editions published in 2005 in English and held by 53 WorldCat member libraries worldwide

Lectures on probability theory by D Bakry( Book )

3 editions published in 1994 in 3 languages and held by 46 WorldCat member libraries worldwide

Markov semigroups at Saint-Flour by D Bakry( Book )

7 editions published in 2012 in English and held by 42 WorldCat member libraries worldwide

Potential theory and stochastics in Albac : Aurel Cornea memorial volume : conference proceedings, Albac, September 4-8, 2007 by ( Book )

7 editions published in 2009 in English and held by 35 WorldCat member libraries worldwide

This volume contains the proceedings of the Potential Theory and Stochastics Conference, which was held in Albac, Romania, from September 4 to 8, 2007. It is also intended as a memorial volume for Aurel Cornea. Besides a presentationof the life and work of Aurel Cornea, it includes twenty refereed papers of the participants, covering the main topics of the conference: geometric aspects in potential theory, Dirichlet structures and stochastic analysis, potential theoretical methods for the analysis of infinite dimensional processes, stochastic partial differential equations, non-linear partial differential equations and potential theory
Analysis and geometry of Markov diffusion operators by D Bakry( )

9 editions published between 2013 and 2014 in English and held by 19 WorldCat member libraries worldwide

The present volume is an extensive monograph on the analytic and geometric aspects of Markov diffusion operators. It focuses on the geometric curvature properties of the underlying structure in order to study convergence to equilibrium, spectral bounds, functional inequalities such as Poincaré, Sobolev or logarithmic Sobolev inequalities, and various bounds on solutions of evolution equations. At the same time, it covers a large class of evolution and partial differential equations. The book is intended to serve as an introduction to the subject and to be accessible for beginning and advanced scientists and non-specialists. Simultaneously, it covers a wide range of results and techniques from the early developments in the mid-eighties to the latest achievements. As such, students and researchers interested in the modern aspects of Markov diffusion operators and semigroups and their connections to analytic functional inequalities, probabilistic convergence to equilibrium and geometric curvature will find it especially useful. Selected chapters can also be used for advanced courses on the topic
Hypercontractivite et integrales singulieres pour les semigroupes de diffusion symetriques by D Bakry( Book )

3 editions published in 1985 in French and Undetermined and held by 14 WorldCat member libraries worldwide

Estimations de la densité du processus du recuit simulé by Didier Concordet( Book )

2 editions published in 1992 in French and held by 4 WorldCat member libraries worldwide

EN UTILISANT LA METHODE DE SOBOLEV FAIBLE DE BAKRY-MICHEL, NOUS ETUDIONS LA VITESSE DE CONVERGENCE DU PROCESSUS DE RECUIT SIMULE EN TEMPS CONTINU, DEFINI SUR UNE VARIETE RIEMANNIENNE COMPACTE ET SUR UN ESPACE FINI, QUAND LA TEMPERATURE TEND VERS ZERO. A PARTIR D'INEGALITES DE SOBOLEV SOUS LA MESURE INITIALE ET DE LA CONNAISSANCE D'UNE ESTIMATION ASYMPTOTIQUE DU TROU SPECTRAL DU GENERATEUR INFINITESIMAL DU PROCESSUS, DES INEGALITES DE SOBOLEV FAIBLES TENDUES SONT CONSTRUITES SOUS LA MESURE INVARIANTE INSTANTANEE. DEUX FAMILLES D'INEGALITES ENTRE ENERGIE ET ENTROPIE DU SYSTEME SONT ALORS CONSTRUITES EN UTILISANT LES INEGALITES DE SOBOLEV FAIBLES TENDUES. GRACE A CELLES-CI LA METHODE DE BAKRY-MICHEL PERMET D'ETUDIER LES VARIATIONS DE LA NORME L#P DE LA DERIVEE DE RADON-NIKODYM DE LA LOI DU PROCESSUS PAR RAPPORT A SA MESURE INVARIANTE INSTANTANEE, LORSQUE P EST UNE FONCTION MONOTONE DU TEMPS QUI TEND RESPECTIVEMENT VERS L'INFINI ET MOINS L'INFINI EN TEMPS FINI. CETTE METHODE CONDUIT A DEUX SYSTEMES DIFFERENTIELS QUI PERMETTENT D'OBTENIR UNE MINORATION ET UNE MAJORATION DE LA DERIVEE DE RADON-NIKODYM DE LA LOI DU PROCESSUS PAR RAPPORT A SA MESURE INVARIANTE INSTANTANEE LORSQUE LA TEMPERATURE TEND VERS ZERO. CES ESTIMATIONS DONNENT DES RENSEIGNEMENTS PRECIS SUR LE COMPORTEMENT DU PROCESSUS EN TEMPS GRAND
Analysis and geometry of Markov diffusion operators by D Bakry( Book )

1 edition published in 2014 in English and held by 3 WorldCat member libraries worldwide

Analysis and geometry of markov diffusion operators by D Bakry( Book )

2 editions published between 2014 and 2016 in English and held by 3 WorldCat member libraries worldwide

CONTRIBUTION A L'ETUDE DES PROCESSUS A DEUX INDICES by D Bakry( Book )

1 edition published in 1980 in French and held by 3 WorldCat member libraries worldwide

Sur les inégalités de Sobolev logarithmiques( Book )

2 editions published in 2000 in French and held by 3 WorldCat member libraries worldwide

Semigroupes de Markov associes a une famille de polynomes orthogonaux by Olivier Mazet( Book )

2 editions published in 1998 in French and held by 2 WorldCat member libraries worldwide

L'OBJET PRINCIPAL DE LA THESE EST L'ETUDE DES SEMIGROUPES DE MARKOV SUR L'ESPACE DE HILBERT DES FONCTIONS DE CARRE INTEGRABLE D'UN ENSEMBLE PROBABILISE, ET PLUS PRECISEMENT LA CARACTERISATION DE LA PROPRIETE DE POSITIVITE, AU MOYEN DE CONSIDERATIONS ET D'OUTILS ALGEBRIQUES. NOUS ETUDIONS EN EFFET LES SEMIGROUPES PAR L'INTERMEDIAIRE DE LEURS DECOMPOSITIONS SPECTRALES SUR UNE BASE DE VECTEURS PROPRES CONVENABLEMENT CHOISIE. NOUS DEMONTRONS L'EQUIVALENCE ENTRE LA PROPRIETE DE POSITIVITE D'UN SEMI-GROUPE ET LA POSITIVITE DU CARRE DU CHAMP ASSOCIE. NOUS CLASSIFIONS ENSUITE LES SEMIGROUPES DE DIFFUSION SUR R, POUR LESQUELS IL EXISTE UNE BASE DE VECTEURS PROPRES DE POLYNOMES ORTHOGONAUX. EN VUE D'ETENDRE CETTE CLASSIFICATION A TOUS LES SEMIGROUPES DE MARKOV, NOUS CARACTERISONS LES VALEURS PROPRES D'UN OPERATEUR POSITIF SUR LA BASE DES POLYNOMES DE HERMITE, PUIS NOUS DONNONS DES DESCRIPTIONS TRAJECTORIELLE ET GEOMETRIQUE DES PROCESSUS ASSOCIES AUX SEMIGROUPES. ENFIN, EN VUE D'ETUDIER DE FACON PLUS GENERALE LE ROLE DE LA BASE DE VECTEURS PROPRES SUR LE SEMIGROUPES DE MARKOV QUI LUI EST ASSOCIE, NOUS TRAITONS LE CAS DE L'ENSEMBLE FINI, ET PLUS PARTICULIEREMENT LES ENSEMBLES DE CARDINAL 2 ET 3
Lectures on probability theory : Ecole d'été de probabilités de Saint-Flour( Book )

1 edition published in 1994 in English and held by 2 WorldCat member libraries worldwide

Analyse des modeles de branchement avec duplication des trajectoires pour l'étude des événements rares by Agnès Lagnoux( Book )

2 editions published in 2006 in French and held by 2 WorldCat member libraries worldwide

Nous étudions, dans cette thèse, le modèle de branchement avec duplication des trajectoires d'abord introduit pour l'étude des événements rares destiné à accélérer la simulation. Dans cette technique, les échantillons sont dupliqués en R copies à différents niveaux pendant la simulation. L'optimisation de l'algorithme à coût fixé suggère de prendre les probabilités de transition entre les niveaux égales à une constante et de dupliquer un nombre égal à l'inverse de cette constante, nombre qui peut être non entier. Nous étudions d'abord la sensibilité de l'erreur relative entre la probabilité d'intérêt P(A) et son estimateur en fonction de la stratégie adoptée pour avoir des nombres de retirage entiers. Ensuite, puisqu'en pratique les probabilités de transition sont généralement inconnues (et de même pour les nombres de retirages), nous proposons un algorithme en deux étapes pour contourner ce problème. Des applications numériques et comparaisons avec d'autres modèles sont proposés
Inégalités fonctionnelles liées aux formes de Dirichlet : de l'isopérimétrie aux inégalités de Sobolev by Pierre Fougères( Book )

2 editions published in 2002 in French and held by 2 WorldCat member libraries worldwide

Les semi-groupes de Markov ergodiques permettent d'approcher des mesures de probabilité au moyen d'inégalités fonctionnelles. L'objectif de la thèse est l'étude de certaines de ces inégalités, de l'isopérimétrie gaussienne aux inégalités de Sobolev. Nous cherchons essentiellement à établir des liens entre elles, à déterminer leurs constantes optimales et à obtenir des critères assurant leur existence. Le travail est divisé en trois parties. Dans la première , nous nous intéressons aux liens entre les inégalités de Sobolev logarithmiques (SL) et celles d'isopérimétrie gaussienne de Bobkov (IGB). Nous montrons qu'un semi-groupe de courbure minorée (éventuellement négative) qui satisfait à (SL) vérifie également une inégalité (IGB). Nous obtenons ainsi une inégalité (IGB) pour certains systèmes de spins. Dans la seconde partie, nous montrons que la constante de Poincaré d'une mesure de probabilité log-concave sur la droite réelle est universellement comparable au carré de la distance moyenne à la médiane
Modélisation probabiliste des écoulements atmosphériques turbulents afin d'en filtrer la mesure par approche particulaire by Christophe Baehr( Book )

2 editions published in 2008 in French and held by 2 WorldCat member libraries worldwide

Non-linear filtering of local turbulent fluid measurements was an unexplored domain, we have developed stochastic modelings and efficient filters. We have defined and studied the acquisition process of a vector field along a random path. We propose non-linear filters for mean-field processes and prove the convergence of their particle approximations. We deeply modify the Lagrangian models of fluids proposed by the physicists to make them compatible with the problem of filtering, the closure of these equations was obtained by conditioning the dynamics to the observation and to the acquisition process. Our algorithm allowed us to filter velocity measurements of a turbulent fluid, simulated or real in 1D to 3D flows
Polynômes orthogonaux associés à la courbe deltoïde by Olfa Zribi( Book )

2 editions published between 2014 and 2015 in French and held by 2 WorldCat member libraries worldwide

The purpose of this thesis is to study the families of orthogonal polynomials associated with the deltoid curve (or Steiner' hypocycloid) in the plane, which are eigenvectors of a differential diffusion operator. These orthogonal polynomials are related to root system A2, to the symmetries of a planar triangular lattice, as well as the spectra of SU(3) matrices. We give first recurrence formulas, generating functions, as well as representations of polynomials in special cases. We then turn to the curvaturedimension inequality satisfied by the associated operator, which allows us to obtain uniform bounds on these polynomials and various characterizations of associated Sobolev inequalities. We then study the h-transformations, which are related to the processes conditioned to stay in a given domain. We show that in general, when a diffusion operator has polynomials eigenvectors, he always have explicit h- transformations. We give of course the example of the deltoid, but also many other examples that fall within this framework, some are classical and other less. Finally, we study the hypergroup properties associated with these operators. These properties leads to the description of all Markov kernels associated with the polynomials. We show that this property is satisfied in a particular form, for polynomials associated with the deltoid, which gives us the first example of hypergroup associated with a root system An
Inégalités fonctionnelles pour des noyaux de la chaleur sous-elliptiques by Michel Bonnefont( Book )

2 editions published in 2009 in French and held by 2 WorldCat member libraries worldwide

In this thesis, I have studied the heat kernel, the heat semigroup and the associated functional inequalities on three model spaces in subelliptic geometry. The main interest of this study is in fact to develop new methods and new technics that we hope we can extend in subelliptic geometry. The real goal is to understand a notion of Ricci curvature bounded below by a constant in subelliptic geometry. Here, the three model spaces are 3-dimensional Lie groups: the Heisenberg group, the SU(2) group and the SL(2,R) group endowed with a sublaplacian: a left-invariant second order differential opertor, self-adjoint with respect to the Haar mesure of the group, which is not elliptic but hypoelliptic from Hörmander's results. My results first concern the setting of explicit formulas for the above heat kernels. Then I focus on the generalisation in subelliptic geometry of the notion of Ricci curvature bounded below by a constant. In this way, I give a generalized Bakry-Emery curvature-dimension criterion which under some antisymetrical conditions satisfied by our model spaces, implies some Li-Yau type estimates. I also study the setting and the consequences of subcommutation inequalities between the gradient and the semigroup. In particular, I give two new proofs of the H.Q.Li inequality on the Heisenberg group
 
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Analysis and geometry of Markov diffusion operators Analysis and geometry of Markov diffusion operators Analysis and geometry of Markov diffusion operators
Covers
Lectures on probability theory : Ecole d'été de probabilités de Saint-Flour XXII, 1992Lectures on probability theoryMarkov semigroups at Saint-FlourPotential theory and stochastics in Albac : Aurel Cornea memorial volume : conference proceedings, Albac, September 4-8, 2007Analysis and geometry of Markov diffusion operatorsAnalysis and geometry of Markov diffusion operatorsAnalysis and geometry of markov diffusion operatorsLectures on probability theory : Ecole d'été de probabilités de Saint-Flour
Alternative Names
Bakry, D.

Bakry, Dominique

Bakry, Roger-Dominique

Dominique Bakry Frans wiskundige

Dominique Bakry fransk matematiker

Dominique Bakry französischer Mathematiker

Dominique Bakry French mathematician

Dominique Bakry matemàtic francès

Dominique Bakry matemático francês

Dominique Bakry matematico francese

Dominique Bakry matemáticu francés

Dominique Bakry mathématicien français

Languages