Lectures related to Martingales and Brownian Motion: Three Stopping Theorems

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

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

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Explores propositions, proofs, and contraposition in mathematical theory, emphasizing logical rules and proof methods.

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

Covers the proof of the martingale convergence theorem and the convergence of the martingale sequence almost surely.

Explores the optional stopping theorem for martingales and stepping times, emphasizing its applications and implications.

Covers the basics of propositional logic, logical connectives, truth tables, and compound propositions.

Explores stopping times in martingales and Brownian motion, discussing convergence properties and the strong Markov property.

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

Covers the basics of discrete mathematics, including logic, structures, and algorithms.

Explores stopping times, the optional stopping theorem, F-measurable random variables, and martingales.

Covers propositional logic, truth tables, and problem-solving strategies in discrete mathematics.

Covers propositions, logical connectives, truth tables, and propositional logic language.

Introduces Coq, covering defining propositions, proving theorems, and using tactics.

Covers the reflection principle and martingale writing in simple symmetric random walks.

Covers the criteria for subgroups and provides examples and proofs.

Covers the calculation of scalar products in coordinates and extends the concept to three-dimensional space.

Explores the average time for a Brownian motion to leave an interval and the maximum distribution.

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.