Isotropic transport process on a Riemannian manifold

Pinsky, Mark A.

doi:10.1090/S0002-9947-1976-0402957-2

Isotropic transport process on a Riemannian manifold
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by Mark A. Pinsky

Trans. Amer. Math. Soc. 218 (1976), 353-360

DOI: https://doi.org/10.1090/S0002-9947-1976-0402957-2

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Abstract:

We construct a canonical Markov process on the tangent bundle of a complete Riemannian manifold, which generalizes the isotropic scattering transport process on Euclidean space. By inserting a small parameter it is proved that the transition semigroup converges to the Brownian motion semigroup provided that the latter preserves the class ${C_0}$. The special case of a manifold of negative curvature is considered as an illustration.

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Diffusions et géométrie différentielle globale