Seminar in hybrid format at McGill University room MC 437 or Zoom.

In this talk I will start from a differential equation and show that the deterministic integration theory of Young (1936) is not suitable to give a pathwise description of stochastic differential equations. I will then present the insight by Terry Lyons (1998) that the missing ingredient is the iterated integral of the Brownian motion as well as a Taylor expansion type equation which gives intuition into why this is the correct object. We will then consider the ansatz of controlled paths and how it can be used to set up a fixed point mapping for rough differential equations. If time allows we will look at applications of the theory to Wong-Zakai approximations and fractional Brownian motion.