Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1155715 | Stochastic Processes and their Applications | 2013 | 31 Pages |
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 the boundary condition of this limiting Markov process and prove the convergence.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Mark Freidlin, Wenqing Hu, Alexander Wentzell,