Probability Theory and Stochastic Processes

12 units (3-0-9)  |  first term
Prerequisites: ACM/IDS 104, ACM/EE/IDS 116 or instructor's permission.
This course offers a rigorous introduction to probability and stochastic processes. Emphasis is placed on the interaction between inequalities and limit theorems, as well as contemporary applications in computing and mathematical sciences. Topics include probability measures, random variables and expectation, independence, concentration inequalities, distances between probability measures, modes of convergence, laws of large numbers and central limit theorem, Gaussian and Poisson approximation, conditional expectation and conditional distributions, filtrations, and discrete-time martingales.
Instructor: Tropp

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