A nonstandard form of the rate function for the occupation measure of a Markov chain
The authors prove a large deviation principle with respect to the weak topology for the occupation measures of a particular Markov chain, whose transition kernel is not Feller continuous and does not have a finite dominating measure. Using the weak convergence approach, they explicitly compute the resulting rate function, and find that it differs from the well-known Donsker-Varadhan form. The Markov chain is also an example, where the large deviation principle with the same rate function does not transfer to the strong topology setting.
scientific article; zbMATH DE number 894797