Mathématiques appliquées

The Theory of Martingales course explores a fundamental concept in probability theory with extensive applications in finance, statistics, and various branches of mathematics. It delves into the definition and properties of martingales, focusing on their role in stochastic processes. Key topics include stopping times, the optional stopping theorem, and Doob's martingale inequalities. The course also covers applications of martingales in proving convergence theorems, such as the Strong Law of Large Numbers and the Central Limit Theorem. Through a rigorous mathematical framework, students gain a deep understanding of martingales' behavior and their significance in theoretical and applied contexts.