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Small Mass Limit of a Langevin Equation on a Manifold

Journal article
Authors Jeremiah Birrell
Scott Hottovy
Giovanni Volpe
Jan Wehr
Published in Annales Henri Poincare
Volume 18
Issue 2
Pages 707-755
ISSN 1424-0637
Publication year 2017
Published at
Pages 707-755
Language en
Links https://doi.org/10.1007/s00023-016-...
Subject categories Mathematics, Physical Sciences

Abstract

© 2016, Springer International Publishing. We study damped geodesic motion of a particle of mass m on a Riemannian manifold, in the presence of an external force and noise. Lifting the resulting stochastic differential equation to the orthogonal frame bundle, we prove that, as m→ 0 , its solutions converge to solutions of a limiting equation which includes a noise-induced drift term. A very special case of the main result presents Brownian motion on the manifold as a limit of inertial systems.

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