Advanced Topics in Stochastics Calculus

The goal of the course is to explore stochastic calculus in depth, by extending the study of stochastic integration from Brownian motion to continuous local martingales. Moreover, based on such an extension, we will turn to other important topics such as: generalised Girsanov theorem, local times and Tanaka's formula as an extension of Ito's formula, weak solutions of stochastic differential equations and Stroock-Varadhan martingale problem, propagation of chaos for mean-field particle systems.

Detailed knowledge of stochastic calculus for continuous semimartingales (even in a non-regular context) with an introduction to limit theorems for mean-field particle systems.