The duality-related point of view of Hoeffding for i.i.d. large deviations is extended to the Markov case. This reconciles Koopmans' "function-analytic" view of Markovian large deviations with Boza's "information theoretic" view, and extends the validity of the latter to the not-necessarily-finite case.
"Large Deviations of Functions of Markovian Transitions and Mathematical Programming Duality." Ann. Probab. 7 (5) 874 - 881, October, 1979. https://doi.org/10.1214/aop/1176994947