Martingale Transforms

This lecture covers the concept of martingale transforms, where a sequence of random variables is adapted to a filtration. The instructor explains the definition and properties of martingale transforms, emphasizing their adaptability to different filtrations. The lecture delves into the interpretation of martingale transforms, showcasing their role in predicting future outcomes based on past information. Various examples are provided to illustrate the application of martingale transforms in different scenarios. The lecture concludes with a discussion on optional stopping theorems and their implications in the context of martingale transforms.