Ergodicity, stabilization, and rsingular perturbations for Bellman-Isaacs equations / / Olivier Alvarez, Martino Bardi

• Record Nr.: UNINA9910829068403321
• Autore: Alvarez Olivier <1969->
• Pubbl/distr/stampa: Providence, Rhode Island : , : American Mathematical Society, , 2010; ©2010
• ISBN: 1-4704-0574-1
• Descrizione fisica: 1 online resource (77 p.)
• Collana: Memoirs of the American Mathematical Society, , 0065-9266 ; ; Number 960
• Disciplina: 515/.353
• Soggetti: Singular perturbations (Mathematics); Differential equations, Partial; Differential games
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: "Volume 204, number 960 (fourth of 5 numbers)."
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: ""Contents""; ""Abstract""; ""Chapter 1. Introduction and statement of the problem""; ""1.1. Introduction""; ""1.2. Stochastic differential games and the singular perturbation problem""; ""1.3. The Bellman-Isaacs equations""; ""Chapter 2. Abstract ergodicity, stabilization, and convergence""; ""2.1. Ergodicity and the effective Hamiltonian""; ""2.2. Stabilization and the effective terminal cost""; ""2.3. The general convergence result""; ""Chapter 3. Uncontrolled fast variables and averaging""; ""3.1. Ergodicity""; ""3.2. Stabilization""; ""3.3. Uniform convergence""; ""3.4. An explicit formula for the limit control problem""""Chapter 4. Uniformly nondegenerate fast diffusion""; ""4.1. Ergodicity""; ""4.2. Stabilization""; ""4.3. Uniform convergence""; ""Chapter 5. Hypoelliptic diffusion of the fast variables""; ""5.1. Ergodicity and stabilization""; ""5.2. Uniform convergence""; ""Chapter 6. Controllable fast variables""; ""6.1. Bounded-time controllability and ergodicity""; ""6.2. Stabilization and a formula for the effective initial data""; ""6.3. An explicit formula for the effective Hamiltonian and the limit differential game""; ""6.4. Uniform convergence""""6.5. The reduction order formula for the effective control problem""; ""Chapter 7. Nonresonant fast variables""; ""7.1. Ergodicity""; ""7.2. Stabilization""; ""7.3. Uniform convergence""; ; ""Chapter 8. A counterexample to uniform convergence""; ""Chapter 9. Applications to homogenization""; ""9.1. Periodic homogenization of 1st order H-J equations""; ""9.2. Periodic homogenization of 2nd order equations""; ""Bibliography""