Small mass asymptotic for the motion with vanishing friction

Mark Freidlin, Wenqing Hu and Alexander Wentzell

Stochastic Processes and their Applications, 2013, vol. 123, issue 1, 45-75

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.

Keywords: Smoluchowski–Kramers approximation; Diffusion processes; Weak convergence; Boundary theory of Markov processes (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:1:p:45-75

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DOI: 10.1016/j.spa.2012.08.013

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