Infinitesimal and asymptotic behavior of some relativistic stochastic flow
type: Dataset
description: We study some Lévy processes with values in the isometry group of Minkowski, De Sitter and Anti-de-Sitter space-times. The isometry group is seen as the frame bundle of the space-time and the Lévy processes we consider are some lift of relativistic markovian processes with values in the unitary tangent bundle of the space-time. Theses processes are relativistic in the sense that theirs trajectories are time-like and their generators are invariant by the isometries of the space-time. In the first part of this work we adapt to the case of a general hypoelliptic diffusion a result of Ben Arous and Gradinaru concerning the singularity of the hypoelliptic Green function. We deduce of this a local Wiener criterion for the relativistic diffusion in the isometry group of Minkowski space-time. In the two last parts we are interested to the asymptotic behavior of the stochastic flow associated to these Lévy processes in the different considered space-times. Under a integrability condition on the Lévy measure we compute explicitly the Lyapunov coefficient for such flows in the isometry group of Minkowski space-time. Then, we do a similar work in the context of de Sitter and Anti-de-Sitter space-times limiting ourselves to the case of diffusions. In fine, we explicit the Poisson boundary of the diffusion in the isometry group of de Sitter space-time.
landing page: https://theses.hal.science/tel-00703181
identifier: NNT: 2012STRAD012
keyword: critere-de-wiener
keyword: diffusion-hypoelliptique
keyword: diffusion-relativiste
keyword: infoeu-reposemanticsdoctoralthesis
keyword: levy-processes
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: minkowski-space-time
keyword: processus-de-levy
keyword: relativistic-markovian-processes
keyword: theses
issued: 2026-06-03T21:30:29.935015
modified: 2026-06-03T21:30:29.935030
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

Infinitesimal and asymptotic behavior of some relativistic stochastic flow
type: Distribution
format: HTML
access URL: https://theses.hal.science/tel-00703181
issued: 2026-06-03T21:30:30.026834
modified: 2026-06-03T21:30:29.892874