Jonathan Mattingley, Duke
Stochastic stabilization of ODEs.

I will discuss a a number of systems where the addition of noise leads to the long time stabilization of an otherwise unstable deterministic system. I view these systems as model problems to develop methods to analyses more complicated problems and understand the issues in play. To this end, effort will be me made to produce sharp results. Interestingly, thought the systems relax to equilibrium exponentially fast the system exhibits "intermittent behavior" and an equilibrium density with  algebraic tails. The analysis makes use of local asymptotic analysis to build and "optimal" global Lyapunov function.