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Homogenization and propagation of chaos to a nonlinear diffusion with sticky reflection
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  • Published: September 1995

Homogenization and propagation of chaos to a nonlinear diffusion with sticky reflection

  • Carl Graham1 

Probability Theory and Related Fields volume 101, pages 291–302 (1995)Cite this article

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Summary

We study a process reflecting in a domain. The process follows Wentzell non-sticky boundary conditions while being adsorbed at the boundary at a certain rate with respect to local time and desorbed at a rate with respect to natural time. We show that when the rates go to infinity with a converging ratio, the process converges to a process with sticky reflection having the limit ratio as the sojourn coefficient. We then study a mean-field interacting system of such particles. We show propagation of chaos to a nonlinear diffusion with sticky reflection when we perform this homogenization simultaneously as the number of particles goes to infinity.

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Authors and Affiliations

  1. Centre de Mathématiques Appliquées, Ecole Polytechnique URA CNRS 756, F-91128, Palaiseau, France

    Carl Graham

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  1. Carl Graham
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Graham, C. Homogenization and propagation of chaos to a nonlinear diffusion with sticky reflection. Probab. Th. Rel. Fields 101, 291–302 (1995). https://doi.org/10.1007/BF01200497

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  • Received: 27 April 1993

  • Revised: 12 September 1994

  • Issue Date: September 1995

  • DOI: https://doi.org/10.1007/BF01200497

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Mathematics Subject Classifications (1991)

  • 60F17
  • 60K35
  • 35K60
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