Small Mass Limit of a Langevin Equation on a Manifold

Jeremiah Birrell, Scott Hottovy, Giovanni Volpe, Jan Wehr

Research output: Contribution to journalArticle

7 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)707-755
Number of pages49
JournalAnnales Henri Poincare
Volume18
Issue number2
DOIs
StatePublished - Feb 1 2017

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Limiting Equations
Langevin Equation
Damped
Geodesic
Stochastic Equations
Brownian motion
Riemannian Manifold
Bundle
Differential equation
Converge
Motion
Term
bundles
differential equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics

Cite this

Small Mass Limit of a Langevin Equation on a Manifold. / Birrell, Jeremiah; Hottovy, Scott; Volpe, Giovanni; Wehr, Jan.

In: Annales Henri Poincare, Vol. 18, No. 2, 01.02.2017, p. 707-755.

Research output: Contribution to journalArticle

Birrell, Jeremiah ; Hottovy, Scott ; Volpe, Giovanni ; Wehr, Jan. / Small Mass Limit of a Langevin Equation on a Manifold. In: Annales Henri Poincare. 2017 ; Vol. 18, No. 2. pp. 707-755.
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