| Titre : | Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations | | Type de document : | texte imprimé | | Auteurs : | Olivier ALVAREZ, Auteur ; Martino BARDI, Auteur | | Editeur : | Providence, R. I. [Etats Unis] : American Mathematical Society | | Année de publication : | cop. 2009 | | Collection : | Memoirs of the American Mathematical Society, ISSN 0065-9266 num. 960 | | Importance : | V-77 p. | | ISBN/ISSN/EAN : | 978-0-8218-4715-2 | | Langues : | Anglais | | Catégories : | 35BXX
35Kxx
49N70
93C70
| | Mots-clés : | perturbation singulière jeux différentiels équation différentielle partielle | | Résumé : | We study singular perturbations of optimal stochastic control problems and differential games arising in the dimension reduction of system with multiple time scales. We analyze the uniform convergence of the value functions via the associated Hamilton-Jacobi-Bellman-Isaacs equations, in the framework of viscosity solutions. The crucial properties of ergodicity and stabilization to a constant that the Hamiltonian must possess are formulated as differential games with ergodic cost criteria. They are studied under various different assumptions and with PDE as well as control-theoretic methods. We construct also an explicit example where the convergence is not uniform. Finally we give some applications to the periodic homogenization of Hamilton-Jacobi equations with non-coercive Hamiltonian and of some degenerate parabolic PDEs. | | Note de contenu : | bibliogr. |
Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations [texte imprimé] / Olivier ALVAREZ, Auteur ; Martino BARDI, Auteur . - Providence, R. I. (Etats Unis) : American Mathematical Society, cop. 2009 . - V-77 p.. - ( Memoirs of the American Mathematical Society, ISSN 0065-9266; 960) . ISBN : 978-0-8218-4715-2 Langues : Anglais | Catégories : | 35BXX
35Kxx
49N70
93C70
| | Mots-clés : | perturbation singulière jeux différentiels équation différentielle partielle | | Résumé : | We study singular perturbations of optimal stochastic control problems and differential games arising in the dimension reduction of system with multiple time scales. We analyze the uniform convergence of the value functions via the associated Hamilton-Jacobi-Bellman-Isaacs equations, in the framework of viscosity solutions. The crucial properties of ergodicity and stabilization to a constant that the Hamiltonian must possess are formulated as differential games with ergodic cost criteria. They are studied under various different assumptions and with PDE as well as control-theoretic methods. We construct also an explicit example where the convergence is not uniform. Finally we give some applications to the periodic homogenization of Hamilton-Jacobi equations with non-coercive Hamiltonian and of some degenerate parabolic PDEs. | | Note de contenu : | bibliogr. |
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Affiner la recherche Interroger des sources externesDelay differential equations and dynamical systems (1991)
Ergodicity, stabilization, and singular perturbations for Bellman-Isaacs equations (cop. 2009)
Geometric theory of semilinear parabolic equations (1981)
