Abstract
2007 Abel prize has been awarded to S R S Varadhan for creating a unified theory of large deviations. We attempt to give a flavour of this branch of probability theory, highlighting the role of Varadhan.
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Ramasubramanian, S. Large deviations: An introduction to 2007 Abel prize. Proc Math Sci 118, 161–182 (2008). https://doi.org/10.1007/s12044-008-0009-5
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DOI: https://doi.org/10.1007/s12044-008-0009-5
Keywords
- Large deviation principle (LDP)
- rate function
- Cramer’s theorem
- Sanov’s theorem
- Esscher transform/tilt
- convex conjugates
- Laplace’s method
- Varadhan’s lemma
- weak convergence of probability measures
- empirical distribution
- Himilton-Jacobi equation
- Burger’s equation
- variational formula
- sample path LDP
- Brownian motion/diffusion
- Markov processes
- ergodicity
- Wentzell-Freidlin theory
- exit problem
- Feynman-Kac formula
- occupation time
- principal eigenvalue
- Donsker-Varadhan theory