Stochastic Stability for Flows with Smooth Invariant Measures
  We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows are stochastically stable with respect to perturbations that are associated with homogeneous diffusions. 
Sergiu Aizicovici and Todd Young
math.DS