Lectures related to Optional Stopping Theorem: Martingales and Stepping Times

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

Covers stochastic integrals, emphasizing isometry and continuity properties in martingales and different spaces.

Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.

Explores martingales, adaptability, and stopping times in stochastic processes.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Explores self-financing strategies, asset pricing theorems, and arbitrage opportunities in financial markets.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explores the construction of Brownian motion with continuous trajectories and the dimension of its zero set.