Some general Lorentz covariant operators, associated to the so-called $\Theta$ (or $\Xi$)-relativistic diffusions and making sense in any Lorentzian manifold, have been introduced by Franchi and Le Jan [Comm. Pure Appl. Math. 60 (2007) 187–251], Franchi and Le Jan [Curvature diffusions in general relativity (2010). Unpublished manuscript]. Only a few examples have been studied so far. We provide in this work some nonexplosion criteria for these diffusions, which can be used in generic cases.
"Nonexplosion criteria for relativistic diffusions." Ann. Probab. 40 (5) 2168 - 2196, September 2012. https://doi.org/10.1214/11-AOP672