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.