Explores the concept of martingales and their relation to Brownian motion through symmetric simple random walks and discusses the potential positive outcomes from the current crisis.
Explores convergence criteria for martingales, including almost sure convergence and Cauchy criterion, leading to the first martingale convergence theorem.
Explores the core concepts of Brownian motion, from molecules to cells, including its history, hypothesis versus description, Langevin's solution, and methods for measuring Brownian motion.
Covers Girsanov's Theorem, absolutely continuous measures, and numerical simulation of Stochastic Differential Equations (SDEs) with applications in finance.
