Large Deviations of Infinite Dimensional Markov Processes - Ii Stochastically Perturbed Evolution Equations

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 diierent perspectives and extensions to some known results. When the drift term is semilinear, the rate function is explicitly identiied. The main large deviation theorem 18 3.2. Applications to semilinear stochastic evolution equations 18 4. Rate function representation for semilinear equations 20 Appendix A. Exponential compact containment estimates 21 A.1. A useful probability estimate 21 A.2. Compact containment estimates 21 Appendix B. Hamilton-Jacobi equations on Hilbert spaces 31 B.1. Semigroups on Hilbert spaces 31 B.2. The Tataru distance 32 B.3. Perturbed optimization principle 35 B.4. The comparison principle 36 References 46