In rough stochastic PDE theory of Hairer type,
rough path lifts with respect to the space variable of two-parameter
continuous Gaussian processes play a main role.
A prominent example of such processes is the solution of the stochastic
under the periodic condition.
The main objective of this paper is to show that the law of the spatial
lift of this process
satisfies a Schilder type large deviation principle
on the continuous path space over a geometric rough path space.
This automatically implies Freidlin-Wentzell type Large deviation for
solutions of (scaled) rough stochastic PDEs.
Our method is a "two-parameter version" of Friz-Victoir's.
Back to Rough Paths: Theory and Applications