Generalization of Martingales

This lecture covers the generalization of the Martingale Central Limit Theorem to sub- and supermartingales, discussing the mathematical concepts behind these extensions and their applications in probability theory. The instructor explains the key properties of sub- and supermartingales, such as the conditional expectations and inequalities involved, providing examples to illustrate these concepts. The lecture also delves into the corollaries related to non-negative supermartingales, highlighting the implications of different scenarios on the martingale properties. Overall, the lecture aims to deepen the understanding of martingales beyond the classical framework, offering insights into their broader applicability in stochastic processes.