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arXiv · 1012.3269

Fast transport asymptotics for stochastic RDEs with boundary noise

Sandra Cerrai·Mark Freidlin
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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.

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Sandra Cerrai, Mark Freidlin. 2010-12-15. Fast transport asymptotics for stochastic RDEs with boundary noise. https://doi.org/10.1214/10-aop552

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