Systems of interacting diffusions with partial annihilations through membranes

Wai Tong Fan UW-Madison

Probability mathscidoc:1806.28001

Annals of Probability, 45, 47, 2017
We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface I. This system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. A related interacting random walk model with discrete state spaces has recently been introduced and studied in Chen and Fan (2014). In this paper, we establish the functional law of large numbers for this new system, thereby extending the hydrodynamic limit in Chen and Fan (2014) to reflected diffusions in domains with mixed-type boundary conditions, which include absorption (harvest of electric charges). We employ a new and direct approach that avoids going through the delicate BBGKY hierarchy.
Hydrodynamic limit, interacting diffusion, reflected diffusion, Dirichlet form, annihilation, nonlinear boundary condition, coupled partial differential equation, martingales.
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  title={Systems of interacting diffusions with partial annihilations through membranes},
  author={Wai Tong Fan},
  booktitle={Annals of Probability},
Wai Tong Fan. Systems of interacting diffusions with partial annihilations through membranes. 2017. Vol. 45. In Annals of Probability. pp.47.
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