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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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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DOI: https://doi.org/10.1007/BF01200497
Mathematics Subject Classifications (1991)
- 60F17
- 60K35
- 35K60