Time parameters and Lorentz transformations of relativistic stochastic   processes
  Rules for the transformation of time parameters in relativistic Langevin equations are derived and discussed. In particular, it is shown that, if a coordinate-time parameterized process approaches the relativistic Juttner-Maxwell distribution, the associated proper-time parameterized process converges to a modified momentum distribution, differing by a factor proportional to the inverse energy. 
J\"orn Dunkel, Peter H\"anggi, Stefan Weber