Systems of small-noise stochastic reaction–diffusion equations satisfy a large deviations principle that is uniform over all initial data

Abstract

Large deviations principles characterize the exponential decay rates of the probabilities of rare events. Cerrai and Röckner (2004) proved that systems of stochastic reaction–diffusion equations satisfy a large deviations principle that is uniform over bounded sets of initial data.This paper proves uniform large deviations results for a system of stochastic reaction–diffusion equations in a more general setting than Cerrai and Röckner. Furthermore, this paper identifies two common situations where the large deviations principle is uniform over unbounded sets of initial data, enabling the characterization of Freidlin–Wentzell exit time and exit shape asymptotics from unbounded sets.