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We consider a class of stochastic reaction-diffusion equations also having astochastic perturbation on the boundary and we show that when the diffusionrate is much larger than the rate of reaction, it is possible to replace theSPDE by a suitable one-dimensional stochastic differential equation. Thisreplacement is possible under the assumption of spectral gap for the diffusionand is a result of averaging in the fast spatial transport. We also study thefluctuations around the averaged motion.

Fast transport asymptotics for stochastic RDEs with boundary noise