Systems of interacting diffusions with partial annihilation through membranes
arXiv:1403.5903 · doi:10.1214/15-AOP1047
Abstract
We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface . 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.
Published at http://dx.doi.org/10.1214/15-AOP1047 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
References in corpus (2)
Cited by in corpus (7)
- Fluctuation limit for interacting diffusions with partial annihilations through membranes
- Hydrodynamic limit and Propagation of Chaos for Brownian Particles reflecting from a Newtonian barrier
- Functional central limit theorem for Brownian particles in domains with Robin boundary condition
- Doubly Feller property of Brownian motions with Robin boundary condition
- Transition densities of reflecting Brownian motions on Lipschitz domains
- Correlation function methods for a system of annihilating Brownian particles
- Propagation of Chaos for reflecting diffusions with local-time dependent noise