Student Lectures - All lectures - Probability, Measure & Martingales: Stopped martingales & optional sampling theorems: 3rd Yr Lecture

In this lecture, the fourth of five we are showing from the 'Probability, Measure and Martingales' 3rd year student course, Jan Obloj explores stopping martingales. We show that a stopped martingale remains a martingale, and state and prove Doob’s optional sampling theorem. The second part of the lecture introduces the notion of uniform integrability and related results, including Vitali’s convergence theorem. You can watch the five lectures from the course as they appear on the playlist: https://www.youtube.com/playlist?list=PL4d5ZtfQonW3pGNZ0PtRe8rVVFBloCjxR You can also watch many other student lectures via our main Student Lectures playlist (also check out specific student lectures playlists): https://www.youtube.com/playlist?list=PL4d5ZtfQonW0A4VHeiY0gSkX1QEraaacE All first and second year lectures are followed by tutorials where students meet their tutor in pairs to go through the lecture and associated problem sheet and to talk and think more about the maths. Third and fourth year lectures are followed by classes.