# Student Probability Seminar

#### A brief introduction to forward-backward stochastic differential equations

**Speaker:**
Alex Dunlap, CIMS

**Location:**
TBA

**Date:**
Wednesday, October 21, 2020, 10 a.m.

**Synopsis:**

If you reverse time in an ordinary differential equation with an initial value, you get an ordinary differential equation with a terminal value, which is basically the same thing. But if you reverse time in a stochastic differential equation while not reversing the filtration, then you get a different sort of beast called a backward stochastic differential equation. Coupling a forward and a backward stochastic differential equation together yields the imaginatively-named concept of a forward-backward stochastic differential equation. I'll give a brief introduction to such objects and how they can be used to generalize the Feynman--Kac formula to give probabilistic representations of solutions to quasilinear parabolic PDEs.