Martingales and Brownian Motion

This lecture introduces a new approach to understanding Brownian motion through discrete objects, specifically symmetric simple random walks. By studying the probabilities of these walks, the lecture explores the concept of martingales and their relation to Brownian motion. The instructor explains the Chapman-Kolmogorov equation and the properties of Brownian motion, emphasizing the continuity of functions and the invariance by translation in space. The lecture concludes with a discussion on the potential positive outcomes that may arise from the current crisis, drawing parallels to historical events and predicting future cycles of highs and lows.