Small Mass Limit of a Langevin Equation on a Manifold

Jeremiah Birrell; Scott Hottovy; Giovanni Volpe; Jan Wehr

doi:10.1007/s00023-016-0508-3

Small Mass Limit of a Langevin Equation on a Manifold

Jeremiah Birrell
, Scott Hottovy
, Giovanni Volpe
, Jan Wehr

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English (US)
Pages (from-to)	707-755
Number of pages	49
Journal	Annales Henri Poincare
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s00023-016-0508-3
State	Published - Feb 1 2017
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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10.1007/s00023-016-0508-3

Cite this

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AB - 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.

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Small Mass Limit of a Langevin Equation on a Manifold

Abstract

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