COM-417: Advanced probability and applications

Lectures in this course (75)

Explores sub- and supermartingales, stopping times, and their applications in stochastic processes.

Covers the optional stopping theorem for martingales, providing a detailed proof and discussing its implications.

Introduces the martingale convergence theorem and demonstrates its application with examples.

Explores the proof of the martingale convergence theorem and the concept of stopping time in square-integrable martingales.

Covers the proof and recap of the martingale convergence theorem, focusing on the conditions for the existence of a random variable.

Explores the proof of the martingale convergence theorem and the conditions for convergence to a random variable.

Explains the martingale convergence theorem and its applications in probability theory.

Explores the generalization of martingales to sub- and supermartingales with a focus on convergence properties.

Explores the generalization of Martingale Central Limit Theorem to sub- and supermartingales, discussing key properties and corollaries.

Explores Azuma's inequality in martingales with bounded differences and its generalization.

Covers McDiarmid's inequality, providing concentration bounds for functions of independent random variables.

Covers examples of cumulative distribution functions for continuous random variables and correlations between random variables.

Explains the independence of events and sets in an algebraic context.

Explores convergence in distribution of random variables and characteristic functions.

Explores branching processes, R0, and R in virus spread control.

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