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.
Fast transport asymptotics for stochastic RDE's with boundary noise / S. Cerrai; M. Freidlin. - In: ANNALS OF PROBABILITY. - ISSN 0091-1798. - STAMPA. - 39:(2011), pp. 369-405. [10.1214/10-AOP552]
Fast transport asymptotics for stochastic RDE's with boundary noise
CERRAI, SANDRA;
2011
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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