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 language||English (US)|
|State||Published - Sep 5 2018|
- Langevin equation
- Noise-induced drift
- Small-mass limit
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