Small mass asymptotic for the motion with vanishing friction

Mark Freidlin, Wenqing Hu, Alexander Wentzell

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)45-75
Number of pages31
JournalStochastic Processes and their Applications
Volume123
Issue number1
DOIs
StatePublished - Jan 2013

Bibliographical note

Funding Information:
This work is supported in part by NSF Grants DMS-0803287 and DMS-0854982 .

Keywords

  • Boundary theory of Markov processes
  • Diffusion processes
  • Smoluchowski-Kramers approximation
  • Weak convergence

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