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Small mass asymptotic for the motion with vanishing friction

Author

Listed:
  • Freidlin, Mark
  • Hu, Wenqing
  • Wentzell, Alexander

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.

Suggested Citation

  • Freidlin, Mark & Hu, Wenqing & Wentzell, Alexander, 2013. "Small mass asymptotic for the motion with vanishing friction," Stochastic Processes and their Applications, Elsevier, vol. 123(1), pages 45-75.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:1:p:45-75
    DOI: 10.1016/j.spa.2012.08.013
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    Cited by:

    1. Wenqing Hu, 2020. "On the Long-Time Behavior of a Perturbed Conservative System with Degeneracy," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1266-1295, September.
    2. Xie, Longjie & Yang, Li, 2022. "The Smoluchowski–Kramers limits of stochastic differential equations with irregular coefficients," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 91-115.

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