How stopping time preserves the balance of a martingale
In this advanced lecture from Oxford Mathematics, Jan Obloj explores the mathematical stability of martingales when they are stopped, alongside the fundamental principles of uniform integrability.
Part of a third-year course, this lecture examines the mechanics of stopped martingales, demonstrating that they retain their martingale property. The session covers the formal statement and proof of Doob’s optional sampling theorem, a cornerstone of probability theory.
The lecture also delves into the concept of uniform integrability and its associated results, specifically focusing on Vitali’s convergence theorem. This provides a deeper look into the convergence properties necessary for rigorous probabilistic analysis.
Source: Probability, Measure & Martingales: Stopped martingales & optional sampling theorems: 3rd Yr Lecture
