2026/2027
Введение в большие уклонения
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Где читается:
Факультет математики
Когда читается:
2 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Язык:
английский
Кредиты:
3
Контактные часы:
20
Course Syllabus
Abstract
The theory of large deviations underwent a spectacular development in the middle of the last century, driven by various independent groups of researchers. In particular, Donsker and Varadhan studied the large-time asymptotics of empirical measures for Markov processes, while Freidlin and Wentzell investigated the vanishing noise limit of stationary distributions for diffusion processes.
The aim of this course is to give an elementary introduction to the theory of large deviations and to show how it can be applied to study qualitative properties of discrete-time dynamical systems with small noise. In particular, we shall prove convergence of trajectories under the vanishing noise limit and study their deviations from their limits. In the case when the deterministic system has a globally stable equilibrium, we show that the stationary distributions satisfy the large deviation principle and describe the associated rate function.