Convergence to the time average by stochastic regularization
  We compare the rate of convergence to the time average of a function over an integrable Hamiltonian flow with the one obtained by a stochastic perturbation of the same flow. Precisely, we provide detailed estimates in different Fourier norms and we prove the convergence even in a Sobolev norm for a special vanishing limit of the stochastic perturbation. 
Olga Bernardi, Franco Cardin and Massimiliano Guzzo
math.DS math.AP