For stochastic differential equations with jumps, we prove that W1H transportation inequalities hold for their invariant probability measures and for their process-level laws on the right-continuous path space w.r.t. the L1-metric and uniform metric, under dissipative conditions, via Malliavin...

In this paper, we consider a uniformly ergodic Markov process (Xn)n[greater-or-equal, slanted]0 valued in a measurable subset E of Rd with the unique invariant measure , where the density f is unknown. We establish the large deviation estimations for the nonparametric kernel density estimator in...

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...

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...