Reductions and deviations for stochastic partial differential equations under fast dynamical boundary conditions
Abstract
In order to understand the impact of random influences at physical boundary on the evolution of multiscale systems, a stochastic partial differential equation model under a fast random dynamical boundary condition is investigated. The noises in the model and in the boundary condition are both additive. An effective equation is derived and justified by reducing the random \emph{dynamical} boundary condition to a simpler one. The effective system is still a stochastic partial differential equation. Furthermore, the quantitative comparison between the solution of the original stochastic system and the effective solution is provided by establishing normal deviations and large deviations principles. Namely, the normal deviations are asymptotically characterized, while the rate and speed of the large deviations are estimated.
Keywords
Cite
@article{arxiv.math/0703042,
title = {Reductions and deviations for stochastic partial differential equations under fast dynamical boundary conditions},
author = {Wei Wang and Jinqiao Duan},
journal= {arXiv preprint arXiv:math/0703042},
year = {2008}
}
Comments
This is a revised version with 29 pages. To appear in Stochastic Analysis and Applications, 2008