Volume 19, 2015
|Page(s)||502 - 514|
|Published online||11 November 2015|
Poisson boundary of a relativistic diffusion in curved space-times: an example
IRMAR, Université Rennes 1, Campus de Beaulieu, 35042
Received: 10 February 2013
Revised: 16 April 2013
We study in details the long-time asymptotic behavior of a relativistic diffusion taking values in the unitary tangent bundle of a curved Lorentzian manifold, namely a spatially flat and fast expanding Robertson–Walker space-time. We prove in particular that the Poisson boundary of the diffusion can be identified with the causal boundary of the underlying manifold.
Mathematics Subject Classification: 60J60 / 60J45 / 83F05
Key words: Relativistic diffusion / lorentzian manifolds / poisson boundary / causal boundary
© EDP Sciences, SMAI, 2015
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