|Course Archives Theoretical Statistics and Mathematics Unit|
Course: Topics in Gaussian Processes
Time: Currently not offered
| Syllabus |
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
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[ Semester Schedule ][ SMU ] [Indian Statistical Institute]