Course Archives Theoretical Statistics and Mathematics Unit | |||
Course: Topics in Gaussian Processes Level: Postgraduate Time: Currently not offered |
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Syllabus Past Exams Summary:The course will provide an introduction to the study of one of the fundamental objects in probability - Gaussian processes. Syllabus: Gaussian processes. Variance bounds, Poincare inequality, Isoperimetric inequality, Log-sobolev inequality, Concentration and transport inequalities. Maxima of Gaussian processes. Majorizing measures and Generic chaining. Excursion probabilities. Hypercontractivity. Additional Topics (depending on time and audience interest): Geometry of Gaussian random fields. Stein's method. Introduction to Malliavin calculus. Pre-requisites: Measure-theoretic probability, Advanced probability (elective) Basic functional analysis and topology. It is mandatory to do Stochastic Processes (elective) in parallel. Suggested Texts : 1. Ramon van Handel : Probability in high dimensions : Notes 2. Manjunath Krishnapur's course on Gaussian processes : Notes 3. R. J. Adler : Introduction to continuity, extrema and related topics for general Gaussian processes. 4. R.J. Adler and J. E. Taylor : Random fields and Geometry. 5. M. Talagrand : Upper and lower bounds for stochastic processes. Top of the page Past Exams | |||
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