03562nam 2200601 450 991048023060332120170822144126.01-4704-0574-1(CKB)3360000000465144(EBL)3114240(SSID)ssj0000888908(PQKBManifestationID)11453154(PQKBTitleCode)TC0000888908(PQKBWorkID)10875125(PQKB)10615845(MiAaPQ)EBC3114240(PPN)195418492(EXLCZ)99336000000046514420150416h20102010 uy 0engur|n|---|||||txtccrErgodicity, stabilization, and rsingular perturbations for Bellman-Isaacs equations /Olivier Alvarez, Martino BardiProvidence, Rhode Island :American Mathematical Society,2010.©20101 online resource (77 p.)Memoirs of the American Mathematical Society,0065-9266 ;Number 960"Volume 204, number 960 (fourth of 5 numbers)."0-8218-4715-5 Includes bibliographical references.""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""Memoirs of the American Mathematical Society ;Number 960.Singular perturbations (Mathematics)Differential equations, PartialDifferential gamesElectronic books.Singular perturbations (Mathematics)Differential equations, Partial.Differential games.515/.353Alvarez Olivier1969-950521Bardi M(Martino),MiAaPQMiAaPQMiAaPQBOOK9910480230603321Ergodicity, stabilization, and rsingular perturbations for Bellman-Isaacs equations2149159UNINA