Course Archives Theoretical Statistics and Mathematics Unit

Course: Theory of Large Deviations Time: Currently not offered Level: Postgraduate Teaching: https://sites.google.com/view/parthanilroy/home/teaching/large-dev

Syllabus Past Exams Syllabus: Introduction to large deviations. Motivations from insurance and statistics. Classical large deviation for partial sums in the Gaussian case: exact computation using Mills ratio. Fenchel-Legendre transform: definition, properties and computation. Cramer’s theorem for general random variables and vectors. General notion of large deviation principle on Polish spaces: Laplace principle, Varadhan’s lemma, weak large deviation principle, exponential tightness, goodness of rate function, contraction principle. Applications. Gartner and Ellis theorem. Sanov’s theorem : Donsker-Varadhan variational formula (if time permits) Prerequisites: Measure Theoretic Probability Advanced Probability Suggested Texts : 1. Large Deviations Techniques and Application by Dembo and Zeitouni 2. Large Deviations by Deuschel and Stroock 3. Large Deviations by Hollander 4. Large Deviations and Applications by Varadhan 5. A Weak Convergence Approach to the Theory of Large Deviations by Dupuis and Ellis Top of the page Past Exams

Midterm 15.pdf 17.pdf 19.pdf

Semestral 15.pdf 17.pdf 19.pdf

Supplementary and Back Paper 15.pdf 19.pdf Top of the page

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