In this paper, we prove the large deviation principle (LDP) for the occupation measures of not necessarily irreducible random dynamical systems driven by Markov processes. The LDP for not necessarily irreducible dynamical systems driven by i.i.d. sequence is derived. As a further application we...

Let (Xn)n=1 be a sequence of i.i.d.r.v.'s with values in a Polish space of law [mu]. Consider the empirical measures . Our purpose is to generalize Sanov's theorem about the large deviation principle of Ln from the weak convergence topology to the stronger Wasserstein metric Wp. We show that Ln...

The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.

A classical damping Hamiltonian system perturbed by a random force is considered. The locally uniform large deviation principle of Donsker and Varadhan is established for its occupation empirical measures for large time, under the condition, roughly speaking, that the force driven by the...