Large deviations for occupation measures of Markov processes: discrete time, noncompact case

A simple proof of the Donsker–Varadhan large-deviation principle for occupation measures of Markov process valued in $\mathbf{R}$ with discrete time is given. A proof is based on a new version of the Dupui–Ellis large-deviation principle for two-dimensional occupation measures. In our setting, the existence of the invariant measure is not assumed. This condition is replaced (from the point of view of applications) by a more natural one. An example of a Markov process defined by nonlinear recursion, for which sufficient conditions of the existence of the large-deviation principle are easily verified, is given.