From Riemannian to Relativistic Diffusions

Jacques Franchi ()
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Jacques Franchi: Université de Strasbourg et CNRS, Institut de Recherche Mathématique Avancée

A chapter in From Riemann to Differential Geometry and Relativity, 2017, pp 481-511 from Springer

Abstract: Abstract We first introduce Euclidean and Riemannian Brownian motions. Then considering Minkowski space, we present the Dudley relativistic diffusion. Finally we construct a family of covariant relativistic diffusions on a generic Lorentz manifold, the quadratic variation of which can be locally determined by the curvature (which allows the interpretation of the diffusion effect on a particle by its interaction with the ambient space-time). Examples are considered, in some classical space-time models: Schwarzschild, Gödel and Robertson-Walker manifolds.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-60039-0_16

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DOI: 10.1007/978-3-319-60039-0_16

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