The lecture adresses classical concepts from probability theory, filling gaps from previous lectures and advancing towards continuous time stochastic processes. We will discuss martingales and their convergence theory (including a proof of the law of large numbers), weak convergence theory (including a proof of the central limit theorem) and then proceed towards the Brownian motion (including the Donsker theorem).
Here are the videos from 2021. The lecture will only be optimized, keeping the core of 2021. About 80% should stay the same.