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Abstract. Convergence of certain transforms of Markov processes generators implies large deviations. In this article, we apply abstract theorems of such type to stochastic evolution equations in real separable Hilbert space, giving different perspectives a

LARGE DEVIATIONS OF INFINITE DIMENSIONAL MARKOV PROCESSES - II STOCHASTICALLY PERTURBED EVOLUTION EQUATIONS JIN FENG Abstract. Convergence of certain transforms of Markov processes generators implies large deviations. In this article, we apply abstract theorems of such type to stochastic evolution equations in real separable Hilbert space, giving di erent perspectives and extensions to some known results. When the drift term is semilinear, the rate function is explicitly identi ed.

Date: 10/15/00. 2000 Mathematics Subject Classi cation. Primary 60F10; Secondary 60J25, 49L25, 60G99. Key words and phrases. large deviations, stochastic evolution equations, viscosity solutions. Work supported in part by NSF Summer Intern Probability Program at the University of Wisconsin Madison, years 1999 and 2000. 1

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