  We define and study on Lorentz manifolds a family of covariant diffusions in
which the quadratic variation is locally determined by the curvature. This
allows the interpretation of the diffusion effect on a particle by its
interaction with the ambient space-time. We will focus on the case of warped
products, especially Robertson-Walker manifolds, and analyse their asymptotic
behaviour in the case of Einstein-de Sitter-like manifolds.
