Fast transport asymptotics for stochastic RDEs with boundary noise
arXiv:1012.3269 · doi:10.1214/10-AOP552
Abstract
We consider a class of stochastic reaction-diffusion equations also having a stochastic perturbation on the boundary and we show that when the diffusion rate is much larger than the rate of reaction, it is possible to replace the SPDE by a suitable one-dimensional stochastic differential equation. This replacement is possible under the assumption of spectral gap for the diffusion and is a result of averaging in the fast spatial transport. We also study the fluctuations around the averaged motion.
Published in at http://dx.doi.org/10.1214/10-AOP552 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)