Nonexplosion criteria for relativistic diffusions

TL;DR

This paper establishes criteria to determine when certain Lorentz covariant relativistic diffusions do not explode, broadening understanding of their behavior in general Lorentzian manifolds.

Contribution

It provides general nonexplosion criteria for \\Theta (or \\Xi)-relativistic diffusions, extending previous specific examples to more generic cases.

Findings

Derived nonexplosion conditions applicable in broad settings

Extended analysis of Lorentz covariant diffusions in general manifolds

Enhanced understanding of the stability of relativistic stochastic processes

Abstract

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 Unpublished manuscript].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.