Fast transport asymptotics for stochastic RDEs with boundary noise

Details Fast transport asymptotics for stochastic RDEs with boundary noise Fast transport asymptotics for stochastic RDEs with boundary noise

2010-12-15

arxiv.org/abs/1012.3269v1

Annals of Probability 2011, Vol. 39, No. 1, 369-405

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP552 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP552

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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