Moderate deviations for systems of slow-fast stochastic reaction-diffusion equations

A Moderate Deviation Principle (MDP) concerns the asymptotic behavior of rare event probabilities that lie on a regime between the Central Limit Theorem and the corresponding Large Deviation Principle (LDP). We study moderate deviations of multiscale systems of stochastic reaction-diffusion equations from the averaging limit. The infinite-dimensional nature of the problem dictates a delicate approach to the proof of the corresponding Laplace Principle. The latter involves the solvability and regularity of solutions to Kolmogorov equations on Hilbert spaces along with finite-dimensional approximation arguments.