Non-explosion criteria for relativistic diffusions

Ismaël Bailleul (1) , Jacques Franchi (2)

1 Statistical Laboratory [Cambridge]
2 IRMA - Institut de Recherche Mathématique Avancée

General Lorentz covariant operators, associated to so-called $\Theta$(or $\Xi$)-relativistic diffusions, and making sense in any Lorentz manifold, were introduced by Franchi and Le Jan in [F-LJ-1], [F-LJ-2]. Only a few examples have been studied. We provide in this work non-explosion criteria for these diffusions, which can be used in generic cases.

Mots clés: Relativistic diffusions; General relativity; Stochastic completeness; Non-explosion criterion; Subriemannian minimal time; Volume growth.; Volume growth

Domaines: Probabilités [math.PR]

Ismaël Bailleul, Jacques Franchi. Non-explosion criteria for relativistic diffusions. 2010. ⟨hal-00501517⟩