Large deviations for stochastic reaction-diffusion systems with multiplicative noise and non-Lipshitz reaction term

Following classical work by Freidlin [Trans. Amer. Math. Soc. (1988) 305 665--657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504--537] and Peszat [Probab. Theory Related Fields (1994) 98 113--136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction--diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, assuming the reaction terms to be only locally Lipschitz with polynomial growth. This generalizes results of the above mentioned authors. Our results apply, in particular, to systems of stochastic Ginzburg--Landau equations with multiplicative noise.