Large Deviations and Adiabatic Transitions for Dynamical Systems and Markov Processes in Fully Coupled Averaging.

Intro -- Contents -- Preface -- Part 1. Hyperbolic Fast Motions -- 1.1. Introduction -- 1.2. Main results -- 1.3. Dynamics of Φ[sup(t)][sub(ε)] -- 1.4. Large deviations: preliminaries -- 1.5. Large deviations: Proof of Theorem 1.2.3 -- 1.6. Further properties of S-functionals -- 1.7. "Very long" time behavior: exits from a domain -- 1.8. Adiabatic transitions between basins of attractors -- 1.9. Averaging in difference equations -- 1.10. Extensions: stochastic resonance -- 1.11. Young measures approach to averaging -- Part 2. Markov Fast Motions -- 2.1. Introduction -- 2.2. Preliminaries and main results -- 2.3. Large deviations -- 2.4. Verifying assumptions for random evolutions -- 2.5. Further properties of S-functionals -- 2.6. "Very long" time behavior: exits from a domain -- 2.7. Adiabatic transitions between basins of attractors -- 2.8. Averaging in difference equations -- 2.9. Extensions: stochastic resonance -- 2.10. Young measures approach to averaging -- Bibliography -- Index.

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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.