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Stochastic processes --- Large deviations. --- Convergence. --- Grandes déviations --- Convergence (Mathématiques) --- Large deviations --- Convergence --- Grandes déviations --- Convergence (Mathématiques)

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The book provides a general introduction to the theory of large deviations and a wide overview of the metastable behaviour of stochastic dynamics. With only minimal prerequisites, the book covers all the main results and brings the reader to the most recent developments. Particular emphasis is given to the fundamental Freidlin-Wentzell results on small random perturbations of dynamical systems. Metastability is first described on physical grounds, following which more rigorous approaches to its description are developed. Many relevant examples are considered from the point of view of the so-called pathwise approach. The first part of the book develops the relevant tools including the theory of large deviations which are then used to provide a physically relevant dynamical description of metastability. Written to be accessible to graduate students, this book provides an excellent route into contemporary research.

Large deviations. --- Stability. --- Dynamics --- Mechanics --- Motion --- Vibration --- Benjamin-Feir instability --- Equilibrium --- Deviations, Large --- Limit theorems (Probability theory) --- Statistics --- Mathematical statistics --- Large deviations --- Stability

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Mathematical statistics --- Limit theorems (Probability theory) --- Fix-point estimation --- Asymptotic efficiencies (Statistics) --- Statistical hypothesis testing --- Large deviations --- Théorèmes limites (Théorie des probabilités) --- Estimation ponctuelle --- Tests d'hypothèses (Statistique) --- Grandes déviations --- Statistics --- Biometry --- Biométrie --- 519.2 --- Probability. Mathematical statistics --- 519.2 Probability. Mathematical statistics --- Théorèmes limites (Théorie des probabilités) --- Tests d'hypothèses (Statistique) --- Grandes déviations --- Biométrie