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.
Original language | English |
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Pages (from-to) | 1299-1371 |
Number of pages | 73 |
Journal | Annals of Applied Probability |
Volume | 27 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jun 2017 |
Externally published | Yes |
Keywords
- Annihilation
- BBGKY hierarchy
- Boundary local time
- Coupled nonlinear partial differential equation
- Duhamel tree expansion
- Heat kernel
- Hydrodynamic limit
- Interacting particle system
- Isoperimetric inequality
- Propagation of chaos
- Random walk
- Reflecting diffusion