Topic: Continuous-Time Martingales

Worked Applications of Doob’s Maximal Inequalities

Uniform Integrability and Class D Martingales

Submartingales, Supermartingales, and Convex Transformations

Stopped Martingales at Bounded Stopping Times

Solved Problems on Optional Stopping and Localization

Right-Continuous Versions of Martingales

Proof of the Bounded Optional Sampling Theorem

Optional Stopping at Unbounded Times Under Uniform Integrability

Optional Stopping Counterexamples and Hypothesis Checks

Nonnegative Local Martingales as Supermartingales