Mastering the convergence and inequalities of martingales
Delve into advanced probability theory with this third-year lecture from Oxford Mathematics. This session covers the technical proofs behind Vitali’s convergence theorem and the essential bounds of Doob’s maximal and Lp inequalities.
Presented by Jan Obloj as part of the 'Probability, Measure and Martingales' course, this lecture completes the proof of Vitali’s convergence theorem. The session also explores how stopping theorems can be extended to the context of uniformly integrable martingales.
The second half of the lecture focuses on establishing the fundamental Doob’s maximal and Lp inequalities. This level of study is part of the Oxford mathematics curriculum, where third-year lectures are typically followed by specialized classes to deepen understanding.
Source: Probability Measure Martingales: Vitali’s convergence theorem, martingale inequalities: Yr 3 Lecture
