Geodesic
A remark on a large deviation theorem for Markov chain with a finite number of states
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 612-622

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We consider the classic problem of large deviations for sums of random variables defined on the states of homogeneous Markov chain with finite phase space. The exact asymptotics for probabilities of large deviations of order $O(\sqrt n)$ is established. The proof is based on application of a local theorem of a new type.
Keywords: conjugate distribution, local theorem, monotone $\varepsilon$-approximation.
Mots-clés : spectrum perturbation 
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     title = {A remark on a large deviation theorem for {Markov} chain with a finite number of states},
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Z. Szewczak. A remark on a large deviation theorem for Markov chain with a finite number of states. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 612-622. http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a16/