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Small Mass Limit of a Langevin Equation on a Manifold


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 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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Correspondence to Jeremiah Birrell.

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Communicated by Christian Maes.

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Birrell, J., Hottovy, S., Volpe, G. et al. Small Mass Limit of a Langevin Equation on a Manifold. Ann. Henri Poincaré 18, 707–755 (2017).

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