Annales Henri Poincaré

, Volume 18, Issue 2, pp 707–755 | Cite as

Small Mass Limit of a Langevin Equation on a Manifold

  • Jeremiah Birrell
  • Scott Hottovy
  • Giovanni Volpe
  • Jan Wehr
Article

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 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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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  • Jeremiah Birrell
    • 1
  • Scott Hottovy
    • 2
  • Giovanni Volpe
    • 3
    • 4
  • Jan Wehr
    • 1
  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA
  2. 2.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA
  3. 3.Soft Matter Lab, Department of PhysicsBilkent UniversityAnkaraTurkey
  4. 4.UNAM, National Nanotechnology Research CenterBilkent UniversityAnkaraTurkey

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