University at Buffalo 3 credits Mathematics
The course covers the theory of large deviations, their applications, and the principles of rare event simulation and variance reduction techniques. The first half of the course starts with combinatorial estimates and centers around Cramer’s and Sanov’s theorems and their counterparts for Markov chains, first in finite-dimensional vector spaces and then in an abstract set-up, touching upon exact asymptotics, moderate deviations, martingale differences and concentration inequalities. The second part of the course focuses on rare event simulation and variance reduction techniques.
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