Stochastic Calculus: Integrals and Processes

This lecture covers stochastic calculus, focusing on stochastic integrals and processes. It starts with Donsker's Theorem, defining Brownian motion and its convergence. The lecture then delves into stochastic integrals, properties, and simple processes. It discusses localization, local martingales, and the uniqueness of Itô decomposition. The lecture concludes with Itô processes, quadratic variation, covariation, and Lévy's Characterization Theorem.