SPDEs on narrow channels and graphs: Convergence and large deviations in case of non smooth noise

Abstract

We investigate a class of stochastic partial differential equations of reaction-diffusion type defined on graphs, which can be derived as the limit of SPDEs on narrow planar channels. In the first part, we demonstrate that this limit can be achieved under less restrictive assumptions on the regularity of the noise, compared to (Cerrai and Freidlin [Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017), 865–899]). In the second part, we establish the validity of a large deviation principle for the SPDEs on the narrow channels and on the graphs, as the width of the narrow channels and the intensity of the noise are jointly vanishing.