Abstract
A new non-conservative stochastic reaction–diffusion system in which two families of random walks in two adjacent domains interact near the interface is introduced and studied in this paper. Such a 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. We show that in the macroscopic limit, the particle densities converge to the solution of a coupled nonlinear heat equations. For this, we first prove that propagation of chaos holds by establishing the uniqueness of a new BBGKY hierarchy. A local central limit theorem for reflected diffusions in bounded Lipschitz domains is also established as a crucial tool.
Citation
Zhen-Qing Chen. Wai-Tong (Louis) Fan. "Hydrodynamic limits and propagation of chaos for interacting random walks in domains." Ann. Appl. Probab. 27 (3) 1299 - 1371, June 2017. https://doi.org/10.1214/16-AAP1208
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