11-08. Martingale theory - Martingale convergence theorem and upcrossing inequality.

In this video, we define the notion of upcrossing of an interval, prove the upcrossing inequality, and deduce from this result the martingale convergence theorem: a supermartingale (or submartingale) bounded in the space of integrable functions converges almost surely to an integrable random variable. This is Section 5.2 of my Stochastic Modeling book. This video is part of the playlist Advanced Stochastic Processes    • 10-01. Stochastic processes - Filtrations,...  .