Lecture
This lecture covers Girsanov's Theorem, absolutely continuous measures, and numerical simulation of Stochastic Differential Equations (SDEs). It explains the motivation behind Girsanov's Theorem, the Radon-Nikodym Theorem, Bayes' Rule, and the Martingale property under change of measure. The lecture also delves into the application of Girsanov's Theorem in the context of the Black-Scholes model, equivalent change of measure, and Novikov's Condition. Furthermore, it discusses the principles of Monte Carlo, discretization schemes for SDEs, and variance reduction techniques.