Course Details

Course details of EE6112
Course NoEE6112
Course TitleTopics in Random Processes and Concentrations
Course Content1. A nuanced look at Conditional Expectations (4 classes) a. The Hilbert Space L2 - covariance as an inner productb. Conditioning on sigma-algebras. Kolmogorov’s Existence Theorem for conditional expectation d. Properties of Conditional Expectations–iterated expectations, MMSE estimator as a projection onto an L2 subspace 2. Filtrations–sequence of sigma-algebras evolving in time (1 class) 3. Random Walks (4 classes) a. Random walks, hitting times, and threshold crossing probabilities, Kingman bound for a G/G/1 queueb. Stopping times and Wald’s identity 4. Martingales (6-8 classes) a. Definitions, basic properties b. Doob’s Optional Stopping Theorem for Martingalesc. Kolmogorov Submartingale Inequality d. Martingale Convergence Theorems and applications (Polya urn, stochastic approximation, population extinction, polar codes etc.) 5. Exchangeability and Zero-One Laws (3-4 classes) a. Exchangeable random variables, de Finetti’s theoremb. Zero-One Laws (Kolmogorov and Hewitt Savage) with applications 6. Concentration of Measure and applications (12-15 classes) a. MGF methods (Chernoff-Hoeffding, Bernstein…) b. Martingale concentrations (Azuma-Hoeffding, Doob’s martingale method, median concentrations) c. Logarithmic Sobolev Inequality d. Talagrand’s Isoperimetric Inequality
Course Offered this semesterNo
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