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February 2016 Asymptotic behavior of a relativistic diffusion in Robertson–Walker space–times
Jürgen Angst
Ann. Inst. H. Poincaré Probab. Statist. 52(1): 376-411 (February 2016). DOI: 10.1214/14-AIHP626

Abstract

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.

Nous déterminons le comportement asymptotique en temps long d’une diffusion relativiste à valeurs dans le fibré tangent unitaire d’un espace de Robertson–Walker. On montre en particulier qu’au voisinage du temps d’explosion de la diffusion, sa projection sur la variété de base converge presque sûrement vers un point aléatoire de la frontière causale et nous décrivons le comportement du vecteur tangent au voisinage de ce point limite.

Citation

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Jürgen Angst. "Asymptotic behavior of a relativistic diffusion in Robertson–Walker space–times." Ann. Inst. H. Poincaré Probab. Statist. 52 (1) 376 - 411, February 2016. https://doi.org/10.1214/14-AIHP626

Information

Received: 19 June 2013; Revised: 1 April 2014; Accepted: 29 April 2014; Published: February 2016
First available in Project Euclid: 6 January 2016

zbMATH: 1344.58017
MathSciNet: MR3449307
Digital Object Identifier: 10.1214/14-AIHP626

Subjects:
Primary: 58J65
Secondary: 53C50, 83F05

Rights: Copyright © 2016 Institut Henri Poincaré

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Vol.52 • No. 1 • February 2016
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