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Conference Stochastic Dynamics (SAMOS, 2007)

Université Paris 1 Panthéon-Sorbonne

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Conference Stochastic Dynamics (SAMOS, 2007)
Conference Stochastic Dynamics (SAMOS, 2007)

Conference Stochastic Dynamics (SAMOS, 2007)

Université Paris 1 Panthéon-Sorbonne

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About Us

Enregistrement des conférences "Stochastic Dynamics" organisées par l'équipe de recherche SAMOS les 11 et 12 juin 2007. Les résumés des intervenants sont également disponibles sur l'Espace pédagogique interactif (http://epi.univ-paris1.fr/samos-conf-stochastic-dynamics). Recommandé à : étudiant de la discipline, chercheur - Catégorie : conférences - Année de réalisation : 2007

Latest Episodes

01 - Intervention du président de l'Université Paris 1 - Pierre-Yves HENIN

Monsieur Pierre-Yves Hénin, Président de l'Université Paris 1, acceuille des participants à la conférence et se félicite que le Centre Pierre Mendès-France serve de cadre à cette manifestation scientifique. Bande son disponible au format mp3 Durée : 6 mn

5 MIN2007 JUN 11
Comments
01 - Intervention du président de l'Université Paris 1 - Pierre-Yves HENIN

02 - Présentation du Centre d'Economie de la Sorbonne - Cuong LE VAN

Monsieur Cuong Le Van, Directeur du Centre d'Economie de la Sorbonne, présente ce centre en décrivant plus particulièrement les thématiques de recherche en mathématiques qui y sont développées. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 10
Comments
02 - Présentation du Centre d'Economie de la Sorbonne - Cuong LE VAN

03 - Property of the density for a three dimensional stochastic wave equation - Marta SANZ-SOLE

Consider the stochastic wave equation in dimension , , where denotes the formal derivative of a Gaussian stationary random field, white in time and correlated in space. Using Malliavin calculus, with Quer-Sardanyons we proved the existence and regularity of density of the law of the solution to the SPDE for any fixed . Denote this density by . More recently, with R. Dalang, we have established joint Hölder continuity in of the sample paths of the solution . On the basis of these two results, we can go further with the study of the properties in of the function , for any fixed . Using a method developed by Watanabe and applied to SPDEs in papers by Morien and Millet and Morien, we prove joint Hölder continuity of of the same order than the sample paths of the solution. We shall explain why the strong degeneracy of the fundamental solution leads to less regularity than one could have expected. Marta SANZ-SOLE. Universitat de Barcelona. Document associé : support de présentation : ...

54 MIN2007 JUN 9
Comments
03 - Property of the density for a three dimensional stochastic wave equation - Marta SANZ-SOLE

04 - Questions - Marta SANZ-SOLE

Marta SANZ-SOLE. Universitat de Barcelona. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 8
Comments
04 - Questions - Marta SANZ-SOLE

05 - Random Attractors and the Preservation of Synchronization in the Presence of Noise - Peter KLOEDEN

The long term behaviour of dissipatively synchronized deterministic systems is determined by the system with the averaged vector field of the original uncoupled systems. This effect is preserved in the presence of environmental i.e., background or additive noise provided stochastic stationary solutions are used instead of steady state solutions. Random dynamical systems and random attractors provide the appropriate mathematical framework for such problems and require Ito stochastic differential equations to be transformed into pathwise random ordinary differential equations. An application to a system of semi-linear parabolic stochastic partial differential equations with additive space-time noise on the union of thin bounded tubular domains separated by a permeable membrane will be considered. What happens with linear multiplicative noise will also be considered. This a joint work with Tomas Caraballo (Sevilla) and Igor Chueshov (Kharkov). Based on the papers T. Caraballo and P.E. ...

38 MIN2007 JUN 7
Comments
05 - Random Attractors and the Preservation of Synchronization in the Presence of Noise - Peter KLOEDEN

06 - Questions - Peter KLOEDEN

Peter KLOEDEN. Johann Wolfgang Goethe University. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 6
Comments
06 - Questions - Peter KLOEDEN

07 - Applications of optimal transport theory to stochastic equations - Lorenzo ZAMBOTTI

We want to present some results on gradient systems with convex potential in finite and infinite dimension. The techniques are based on recent developments in the theory of gradient flows in the Wasserstein metric. (joint work with L. Ambrosio & G. Savaré). Lorenzo ZAMBOTTI. Université Paris 6. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789954236 (pdf) Bande son disponible au format mp3 Durée : 43 mn

42 MIN2007 JUN 5
Comments
07 - Applications of optimal transport theory to stochastic equations - Lorenzo ZAMBOTTI

08 - Questions - Lorenzo ZAMBOTTI

Lorenzo ZAMBOTTI. Université Paris 6. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 4
Comments
08 - Questions - Lorenzo ZAMBOTTI

09 - Reductions and deviations for stochastic partial differential equations under fast dynamical boundary conditions - Jinqiao DUAN

As a model for multiscale systems under random influences on physical boundary, a stochastic partial differential equation under a fast random dynamical boundary condition is investigated. An effective equation is derived and justified by reducing the random dynamical boundary condition to a usual random boundary condition. The effective system is still a stochastic partial differential equation, but is more tractable. Furthermore, the quantitative comparison between the solution of the original stochastic system and the effective solution is provided by estimating deviations. Jinqiao DUAN. Illinois Institute of Technology. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182790011791 (pdf) Bande son disponible au format mp3 Durée : 42 mn

41 MIN2007 JUN 3
Comments
09 - Reductions and deviations for stochastic partial differential equations under fast dynamical boundary conditions - Jinqiao DUAN

10 - Questions - Jinqiao DUAN

Jinqiao DUAN. Illinois Institute of Technology. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 2
Comments
10 - Questions - Jinqiao DUAN

Latest Episodes

01 - Intervention du président de l'Université Paris 1 - Pierre-Yves HENIN

Monsieur Pierre-Yves Hénin, Président de l'Université Paris 1, acceuille des participants à la conférence et se félicite que le Centre Pierre Mendès-France serve de cadre à cette manifestation scientifique. Bande son disponible au format mp3 Durée : 6 mn

5 MIN2007 JUN 11
Comments
01 - Intervention du président de l'Université Paris 1 - Pierre-Yves HENIN

02 - Présentation du Centre d'Economie de la Sorbonne - Cuong LE VAN

Monsieur Cuong Le Van, Directeur du Centre d'Economie de la Sorbonne, présente ce centre en décrivant plus particulièrement les thématiques de recherche en mathématiques qui y sont développées. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 10
Comments
02 - Présentation du Centre d'Economie de la Sorbonne - Cuong LE VAN

03 - Property of the density for a three dimensional stochastic wave equation - Marta SANZ-SOLE

Consider the stochastic wave equation in dimension , , where denotes the formal derivative of a Gaussian stationary random field, white in time and correlated in space. Using Malliavin calculus, with Quer-Sardanyons we proved the existence and regularity of density of the law of the solution to the SPDE for any fixed . Denote this density by . More recently, with R. Dalang, we have established joint Hölder continuity in of the sample paths of the solution . On the basis of these two results, we can go further with the study of the properties in of the function , for any fixed . Using a method developed by Watanabe and applied to SPDEs in papers by Morien and Millet and Morien, we prove joint Hölder continuity of of the same order than the sample paths of the solution. We shall explain why the strong degeneracy of the fundamental solution leads to less regularity than one could have expected. Marta SANZ-SOLE. Universitat de Barcelona. Document associé : support de présentation : ...

54 MIN2007 JUN 9
Comments
03 - Property of the density for a three dimensional stochastic wave equation - Marta SANZ-SOLE

04 - Questions - Marta SANZ-SOLE

Marta SANZ-SOLE. Universitat de Barcelona. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 8
Comments
04 - Questions - Marta SANZ-SOLE

05 - Random Attractors and the Preservation of Synchronization in the Presence of Noise - Peter KLOEDEN

The long term behaviour of dissipatively synchronized deterministic systems is determined by the system with the averaged vector field of the original uncoupled systems. This effect is preserved in the presence of environmental i.e., background or additive noise provided stochastic stationary solutions are used instead of steady state solutions. Random dynamical systems and random attractors provide the appropriate mathematical framework for such problems and require Ito stochastic differential equations to be transformed into pathwise random ordinary differential equations. An application to a system of semi-linear parabolic stochastic partial differential equations with additive space-time noise on the union of thin bounded tubular domains separated by a permeable membrane will be considered. What happens with linear multiplicative noise will also be considered. This a joint work with Tomas Caraballo (Sevilla) and Igor Chueshov (Kharkov). Based on the papers T. Caraballo and P.E. ...

38 MIN2007 JUN 7
Comments
05 - Random Attractors and the Preservation of Synchronization in the Presence of Noise - Peter KLOEDEN

06 - Questions - Peter KLOEDEN

Peter KLOEDEN. Johann Wolfgang Goethe University. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 6
Comments
06 - Questions - Peter KLOEDEN

07 - Applications of optimal transport theory to stochastic equations - Lorenzo ZAMBOTTI

We want to present some results on gradient systems with convex potential in finite and infinite dimension. The techniques are based on recent developments in the theory of gradient flows in the Wasserstein metric. (joint work with L. Ambrosio & G. Savaré). Lorenzo ZAMBOTTI. Université Paris 6. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182789954236 (pdf) Bande son disponible au format mp3 Durée : 43 mn

42 MIN2007 JUN 5
Comments
07 - Applications of optimal transport theory to stochastic equations - Lorenzo ZAMBOTTI

08 - Questions - Lorenzo ZAMBOTTI

Lorenzo ZAMBOTTI. Université Paris 6. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 4
Comments
08 - Questions - Lorenzo ZAMBOTTI

09 - Reductions and deviations for stochastic partial differential equations under fast dynamical boundary conditions - Jinqiao DUAN

As a model for multiscale systems under random influences on physical boundary, a stochastic partial differential equation under a fast random dynamical boundary condition is investigated. An effective equation is derived and justified by reducing the random dynamical boundary condition to a usual random boundary condition. The effective system is still a stochastic partial differential equation, but is more tractable. Furthermore, the quantitative comparison between the solution of the original stochastic system and the effective solution is provided by estimating deviations. Jinqiao DUAN. Illinois Institute of Technology. Document associé : support de présentation : http://epi.univ-paris1.fr/servlet/com.univ.collaboratif.utils.LectureFichiergw?CODE_FICHIER=1182790011791 (pdf) Bande son disponible au format mp3 Durée : 42 mn

41 MIN2007 JUN 3
Comments
09 - Reductions and deviations for stochastic partial differential equations under fast dynamical boundary conditions - Jinqiao DUAN

10 - Questions - Jinqiao DUAN

Jinqiao DUAN. Illinois Institute of Technology. Bande son disponible au format mp3 Durée : 4 mn

3 MIN2007 JUN 2
Comments
10 - Questions - Jinqiao DUAN
hmly
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