Strong and Weak Solutions: Girsanov Theorem

This lecture covers the concept of strong and weak solutions in the context of the Girsanov Theorem, exploring the existence of weak solutions for equations with bounded f and g functions. It delves into constructing functions to demonstrate the absence of strong solutions and the criteria for the existence of weak solutions. The lecture also discusses the independence of Brownian increments and the implications for the distribution of solutions. Additionally, it examines the contradiction that arises when X is adapted, highlighting the importance of filtration in determining the nature of solutions.