Theory of Large Deviations

The theory of large deviations is concerned with the probabilities of very rare events. There are many applications where a rare event can have a significant impact (think of the lottery) and it is of interest to know when and how these events occur. The course will begin with a review of the general framework, standard techniques, and elementary examples (e.g., Cramer's and Sanov's Theorems) before proceeding with general theory and applications. If time permits, the course will end with a study of large deviations for diffusion processes.