Geodesic
Large deviations for occupation measures of Markov processes: discrete time, noncompact case
Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 1, pp. 65-88
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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.
Keywords: large deviations, exponential tightness, locallarge deviations. 
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     author = {R. Sh. Liptser},
     title = {Large deviations for occupation measures of {Markov} processes: discrete time, noncompact case},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {65--88},
     year = {1996},
     volume = {41},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1996_41_1_a3/}
}
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R. Sh. Liptser. Large deviations for occupation measures of Markov processes: discrete time, noncompact case. Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 1, pp. 65-88. http://geodesic.mathdoc.fr/item/TVP_1996_41_1_a3/