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arXiv · 1604.04819

Small Mass Limit of a Langevin Equation on a Manifold

Jeremiah Birrell·Scott Hottovy·Giovanni Volpe·Jan Wehr
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Abstract

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 $m \to 0$, its solutions converge to solutions of a limiting equation which includes a {\it 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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Jeremiah Birrell, Scott Hottovy, Giovanni Volpe, Jan Wehr. 2016-04-17. Small Mass Limit of a Langevin Equation on a Manifold. https://doi.org/10.1007/s00023-016-0508-3

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