Thursday, 03 October, 2013
Prof. David Herzog, Duke University
Abstract: With broad interests in mind, we discuss certain, explosive ODEs in the plane that become stable under the addition of noise. In each equation, the process by which stabilization occurs is intuitively clear: Noise diverts 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 showing stabilization 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.