Poisson boundary of a relativistic diffusion in curved space-times: an   example
  We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson-Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with the causal boundary of the underlying manifold. 
J\"urgen Angst
math.PR math-ph math.DG math.MP