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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Isotropic transport process on a Riemannian manifold


Author: Mark A. Pinsky
Journal: Trans. Amer. Math. Soc. 218 (1976), 353-360
MSC: Primary 60J65; Secondary 58G99
DOI: https://doi.org/10.1090/S0002-9947-1976-0402957-2
MathSciNet review: 0402957
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0402957-2
Keywords: Isotropic transport process, geodesic flow, Brownian motion, contraction semigroup
Article copyright: © Copyright 1976 American Mathematical Society