Ergodicity, Stabilization, and Singular Perturbations for Bellman-Isaacs Equations.

Intro -- 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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.