Stability properties of |Psi|² in Bohmian dynamics

According to Bohmian dynamics, the particles of a quantum system move along trajectories, following a velocity field determined by the wave-function Psi(x,t). We show that for simple one-dimensional systems any initial probability distribution of a statistical ensemble approaches asymptotically |Psi(x,t)}|^2 if the system is subject to a random noise of arbitrarily small intensity.