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Large deviations principles characterize the exponential decay rates of theprobabilities of rare events. Cerrai and Rockner [13] proved that systems ofstochastic reaction-diffusion equations satisfy a large deviations principlethat is uniform over bounded sets of initial data.  This paper proves uniform large deviations results for a system of stochasticreaction--diffusion equations in a more general setting than Cerrai andRockner. Furthermore, this paper identifies two common situations where thelarge deviations principle is uniform over unbounded sets of initial data,enabling the characterization of Freidlin-Wentzell exit time and exit shapeasymptotics from unbounded sets.

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