Small mass asymptotic for the motion with vanishing friction
Probability
2012-09-26 v3 Mathematical Physics
math.MP
Abstract
We consider the small mass asymptotic (Smoluchowski-Kramers approximation) for the Langevin equation with a variable friction coefficient. The friction coefficient is assumed to be vanishing within certain region. We introduce a regularization for this problem and study the limiting motion for the 1-dimensional case and a multidimensional model problem. The limiting motion is a Markov process on a projected space. We specify the generator and boundary condition of this limiting Markov process and prove the convergence.
Keywords
Cite
@article{arxiv.1201.1242,
title = {Small mass asymptotic for the motion with vanishing friction},
author = {Mark Freidlin and Wenqing Hu and Alexander Wentzell},
journal= {arXiv preprint arXiv:1201.1242},
year = {2012}
}
Comments
final version for publication, accepted by Stochastic Processes and their Applications