Asymptotic behavior of a relativistic diffusion in Robertson-Walker space-times

作者：Angst Juergen^*

来源：Annales de l Institut Henri Poincare-Probabilites et Statistiques, 2016, 52(1): 376-411.

DOI：10.1214/14-AIHP626

• Brownian Motion
• Relativistic diffusion
• Robertson-Walker space-times
• Causal boundary

We determine the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a Robertson Walker space time. We prove in particular that when approaching the explosion time of the diffusion, its projection on the base manifold almost surely converges to a random point of the causal boundary and we also describe the behavior of the tangent vector in the neighborhood of this limiting point.

• 出版日期2016-2