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(2017) From Riemann to differential geometry and relativity, Dordrecht, Springer.
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.
Publication details
DOI: 10.1007/978-3-319-60039-0_16
Full citation:
Franchi, J. (2017)., From Riemannian to relativistic diffusions, in L. Ji, A. Papadopoulos & S. Yamada (eds.), From Riemann to differential geometry and relativity, Dordrecht, Springer, pp. 481-511.
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