Langevin equations in the small-mass limit: Higher order approximations

Jeremiah Birrell, Jan Wehr

Research output: Contribution to journalArticlepeer-review

Abstract

We study the small-mass (overdamped) limit of Langevin equations for a particle in a potential and/or magnetic field with matrix-valued and state-dependent drift and diffusion. The present work generalizes prior derivations of the homogenized equation for the position degrees of freedom in the m → 0 limit. Specifically, we develop a hierarchy of approximate equations for the position degrees of freedom that achieves accuracy of order mℓ/2 over compact time intervals for any ℓ ∈ Z+. The results cover bounded forces, for which we prove convergence in Lp norms, and unbounded forces, in which case we prove convergence in probability.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Sep 5 2018

Keywords

  • Homogenization
  • Langevin equation
  • Noise-induced drift
  • Small-mass limit

ASJC Scopus subject areas

  • General

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