On some relativistic-covariant stochastic processes in Lorentzian space-times

摘要

A Lorentz-covariant relativistic Brownian motion has been defined by Dudley in the framework of special relativity, and extended to general relativity by Franchi and Le Jan. It is a random timelike curve of class C-1, the world-line of a particle with an intrinsic (i.e., relativistically covariant) law of motion. Building on the Franchi-Le Jan process, we propose a possible definition for random spacelike curves enjoying relativistic covariance; they are more regular (at least C-2) than the timelike ones. To cite this article: M. Emery, C. R. Acad. Sci. Paris, Ser. I 347 (2009).