Probability, Measure and Martingales - Stopped Martingales and Optional Sampling Theorems

This lecture from the University of Oxford's 'Probability, Measure and Martingales' third-year course explores stopping martingales with Professor Jan Obloj. Discover how a stopped martingale maintains its martingale property, and learn about Doob's optional sampling theorem with complete proofs. The 54-minute session also introduces uniform integrability concepts and Vitali's convergence theorem. This lecture is part of a five-part series available in a dedicated playlist, with the Oxford mathematics program featuring tutorials for first and second-year students (in pairs with tutors) and classes for third and fourth-year students to reinforce lecture content.