Abstract:
I will start with the deterministic dynamics generated by a vector
field that has several unstable critical points connected by
heteroclinic orbits. A perturbation of this system by white noise will
be considered.  I will study the limit of the resulting stochastic
system in distribution (under appropriate time rescaling) as the noise
intensity vanishes. It is possible to describe the limiting process in
detail, and, in particular, interesting non-Markov effects arise.  There
are situations where this result provides more precise exit asymptotics
than the classical Wentzell-Freidlin theory.