Large Deviations of Infinite Dimensionalmarkov Processes

Deterministic evolutions, generated by dissipative operators in Banach spaces, can be characterized using a set of integral inequalities. Such characterization is particularly useful in the nonlinear context. In this paper, we exploit such technique for variational problems appearing in the rate function of large deviation of innnite dimensional processes. We extend the method of rate function representation in Feng and Kurtz 8]. Examples of controlled deterministic evolutions in Hilbert spaces 5 2. A large deviation theorem 11 2.1. Basic setup 11 2.2. A large deviation theorem 11 2.3. Large deviation under a stronger topology 14 3. Controlled equations and variational representation of the rate function 16 3.1. Functional equations for deterministic control problem 16 3.2. The Nisio semigroup 21 3.3. A variational formula and representation of large deviation rate function 21 4. Veriication of rate function representation using generators 25 4.