Student Probability Seminar

Overview of Rough Path Theory

Speaker: Eric Thoma, CIMS

Location: Warren Weaver Hall 1314

Date: Monday, April 8, 2019, 12:30 p.m.


Rough path theory achieves the pathwise construction of stochastic integrals and solutions to SDE. In this talk, I will motivate the analytic framework and give an overview of the central results of the theory. I will discuss how the theory clarifies issues concerning the convergence of noise by proving various Wong-Zakai type theorems. The talk will address the question: why is the Ito integral the "physically correct" integral sometimes, but the Stratonovich integral correct other times? In fact, I will give a concrete example in which neither is "correct". Time permitting, I will discuss how rough path theory leads into theory of regularity structures and of paracontrolled distributions.