Stochastic Stability of Planar Flows

Group Members

Lance Ford, Derek Kielty, Rajeshwari Majumdar, Heather McCain, Dylan O’ConnellREU2015-Stochastics

Supervisors

Joe P ChenFanNy Shum

Overview

We investigated systems of complex-valued ordinary differential equations (ODEs) that blows up in finite time, which we refer to as explosive systems. The goal is to understand for what initial conditions does the system explode and will the addition of noise stabilize it; that is, if we were to perturb the system with an additive Brownian motion, will the system of stochastic differential equation (SDE) still be explosive? In fact, we were able to prove a toy model of the stochastic Burgers’ equation to be ergodic; that is, the SDE is nonexplosive and it has a unique limiting distribution.

Presentation

Poster