Мини-курс "Теория больших уклонений Фрейдлина–Вентцеля" Леонида Коралова
21 апреля начнется онлайн мини-курс "Теория больших уклонений Фрейдлина–Вентцелля" Леонида Коралова (Мэрилендский университет, США).
Lecture 1: Preliminaries: Stochastic integral, Ito's formula, stochastic differential equations, Feynman-Kac formula, Girsanov formula.
Lecture 2: Large deviations for families of measures on a Euclidean space. General definition of the action functional. Large deviations for randomly perturbed dynamical systems.
Lecture 3: Problem on the exit from a domain due to large deviations. Asymptotics of the exit time and the location of the exit point. Randomly perturbed dynamical system with multiple equilibria. Hierarchy of Markov chains construction. Metastability. Systems with metastable behavior.
Lecture 4: Fluctuations in dynamical systems with averaging: averaging principle, normal deviations from the averaged behavior, large deviations from the averaged behavior, not very large deviations.
Lecture 5: Large deviations for random measures. Reaction front propagation for reaction-diffusion equations with small diffusion.