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From Riemannian to Relativistic Diffusions

In: From Riemann to Differential Geometry and Relativity

Author

Listed:
  • Jacques Franchi

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

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.

Suggested Citation

  • Jacques Franchi, 2017. "From Riemannian to Relativistic Diffusions," Springer Books, in: Lizhen Ji & Athanase Papadopoulos & Sumio Yamada (ed.), From Riemann to Differential Geometry and Relativity, pages 481-511, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-60039-0_16
    DOI: 10.1007/978-3-319-60039-0_16
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