The weak large deviations principle holds for empirical measures of non-irreducible Markov chains on R^d with arbitrary initial measure, proved via subadditivity, with the rate function not necessarily convex.
A variational formulation of equilibrium statistical mechanics and the gibbs phase rule.Communications in Mathematical Physics, 5:324–329
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Large deviations for non-irreducible Markov chains on Euclidean spaces
The weak large deviations principle holds for empirical measures of non-irreducible Markov chains on R^d with arbitrary initial measure, proved via subadditivity, with the rate function not necessarily convex.