Department of Mathematical Sciences, Ritsumeikan University Web Page

Date: 17:00–17:50, January 15, 2015
Place: The 4th Lab. of Math. on the 7th floor of West Wing
Speaker: David Herzog (Drake University)
Title: Noise-Induced Stabilization of Planar Flows
Abstract:
We discuss certain, explosive ODEs in the plane that become stable under the additionof noise. In each equation, the process by which stabilization occurs is intuitively clear: Noisediverts the solution away from any instabilities in the underlying ODE. However, in many cases, proving rigorously this phenomenon occurs has thus far been difficult and the current methods used to do so are rather ad hoc. Here we present a general, novel approach to showingstabilization by noise and apply it to these examples. We will see that the methods used streamline existing arguments as well as produce optimal results, in the sense that they allow us to understand well the asymptotic behavior of the equilibrium measure at infinity.