Abstract

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. Roughly speaking, they are characterised by the existence at each (proper) time (of the moving particle) of a (local) rest frame where the random part of the acceleration of the particle (computed using the time of the rest frame) is Brownian in any spacelike direction of the frame.

I will explain how the tools of stochastic calculus enable us to give a concise and elegant description of these random paths on any Lorentzian manifold. A mathematically clear definition of the one-particle distribution function of the dynamics will emerge from this definition, and whose main property will be explained. This will enable me to obtain a general H-theorem and to shed some light on links between probabilistic notions and the large scale structure of the manifold.

All necessary tools from stochastic calculus will be explained.