Small Mass Limit of a Langevin Equation on a Manifold
Jeremiah Birrell, Scott Hottovy, Giovanni Volpe & Jan Wehr
Annales Henri Poincaré 18(2), 707—755 (2017)
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.