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Ergodicity, stabilization, and rsingular perturbations for Bellman-Isaacs equations / / Olivier Alvarez, Martino Bardi
| Ergodicity, stabilization, and rsingular perturbations for Bellman-Isaacs equations / / Olivier Alvarez, Martino Bardi |
| Autore | Alvarez Olivier <1969-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (77 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Singular perturbations (Mathematics)
Differential equations, Partial Differential games |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-0574-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910480230603321 |
Alvarez Olivier <1969->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ergodicity, stabilization, and rsingular perturbations for Bellman-Isaacs equations / / Olivier Alvarez, Martino Bardi
| Ergodicity, stabilization, and rsingular perturbations for Bellman-Isaacs equations / / Olivier Alvarez, Martino Bardi |
| Autore | Alvarez Olivier <1969-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (77 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Singular perturbations (Mathematics)
Differential equations, Partial Differential games |
| ISBN | 1-4704-0574-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910788857903321 |
|
Alvarez Olivier <1969->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Ergodicity, stabilization, and rsingular perturbations for Bellman-Isaacs equations / / Olivier Alvarez, Martino Bardi
| Ergodicity, stabilization, and rsingular perturbations for Bellman-Isaacs equations / / Olivier Alvarez, Martino Bardi |
| Autore | Alvarez Olivier <1969-> |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2010 |
| Descrizione fisica | 1 online resource (77 p.) |
| Disciplina | 515/.353 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Singular perturbations (Mathematics)
Differential equations, Partial Differential games |
| ISBN | 1-4704-0574-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| 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"" |
| Record Nr. | UNINA-9910829068403321 |
|
Alvarez Olivier <1969->
|
||
| Providence, Rhode Island : , : American Mathematical Society, , 2010 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||