Zachary Selk (Queen’s)

PDEs & Applications Seminar

Tuesday, November 21st, 2023

Time: 9:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Zachary Selk (Queen’s)

Title: Stochastic Representations of Solutions of the Wave Equation

Abstract: The Feynman-Kac formula represents solutions to parabolic PDE in a stochastic way through averages of diffusions. It has achieved widespread success in pure mathematics, physics, engineering and numerical methods through Monte-Carlo estimations, leading to thousands of papers since the 1950s. Similarly, solutions of elliptic PDE have stochastic representations through averages of exit times and have again found widespread success. It would be impossible to do justice to the literature of stochastic representations of solutions to either parabolic or elliptic PDE because they have been such vast and successful areas.

However, the hyperbolic case has been largely unstudied. In this talk, I will present a short (6-page!) preprint from Sourav Chaterjee on stochastic solutions to the wave equation https://arxiv.org/abs/1306.2382 It is one of three manuscripts I have found on stochastic solutions to the wave equation. It is insufficient in several ways and leads to several open questions which I will detail.