  A new class of relativistic diffusions encompassing all the previously
studied examples has recently been introduced by C. Chevalier and F. Debbasch,
both in a heuristic and analytic way. A pathwise approach of these processes is
proposed here, in the general framework of Lorentzian geometry. In considering
the dynamics of the random motion in strongly causal spacetimes, we are able to
give a simple definition of the one-particle distribution function associated
with each process of the class and prove its fundamental property. This result
not only provides a dynamical justification of the analytical approach
developped up to now (enabling us to recover many of the results obtained so
far), but it provides a new general H-theorem. It also sheds some light on the
importance of the large scale structure of the manifold in the asymptotic
behaviour of the Franchi-Le Jan process. This pathwise approach is also the
source of many interesting questions that have no analytical counterparts.
