Small mass limit of a langevin equation on a manifold
Date
2017-02
Authors
Birrell, J.
Hottovy, S.
Volpe, G.
Wehr, J.
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Annales Henri Poincare
Print ISSN
1424-0637
Electronic ISSN
Publisher
Birkhauser Verlag AG
Volume
18
Issue
2
Pages
707 - 755
Language
English
Type
Journal Title
Journal ISSN
Volume Title
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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→ 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.