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January 2011 Fast transport asymptotics for stochastic RDEs with boundary noise
Sandra Cerrai, Mark Freidlin
Ann. Probab. 39(1): 369-405 (January 2011). 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.

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Sandra Cerrai. Mark Freidlin. "Fast transport asymptotics for stochastic RDEs with boundary noise." Ann. Probab. 39 (1) 369 - 405, January 2011. https://doi.org/10.1214/10-AOP552

Information

Published: January 2011
First available in Project Euclid: 3 December 2010

zbMATH: 1210.60065
MathSciNet: MR2778806
Digital Object Identifier: 10.1214/10-AOP552

Subjects:
Primary: 35K57 , 35R60 , 60F99 , 60H15

Keywords: averaging , boundary noise , Invariant measures , Multiscaling limits for stochastic reaction-diffusion equations , spectral gap

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.39 • No. 1 • January 2011
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