Fast transport asymptotics for stochastic RDEs with boundary noise

Cerrai, Sandra; Freidlin, Mark

Ann. Probab., Tome 39 (2011) no. 1, p. 369-405 / Harvested from Project Euclid

Résumé

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.

Publié le : 2011-01-15
Classification: Multiscaling limits for stochastic reaction-diffusion equations, boundary noise, invariant measures, spectral gap, averaging, 60H15, 60F99, 35R60, 35K57

@article{1291388305,
     author = {Cerrai, Sandra and Freidlin, Mark},
     title = {Fast transport asymptotics for stochastic RDEs with boundary noise},
     journal = {Ann. Probab.},
     volume = {39},
     number = {1},
     year = {2011},
     pages = { 369-405},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1291388305}
}

Cerrai, Sandra; Freidlin, Mark. Fast transport asymptotics for stochastic RDEs with boundary noise. Ann. Probab., Tome 39 (2011) no. 1, pp.  369-405. http://gdmltest.u-ga.fr/item/1291388305/