Geodesic
Large deviation principle for integral functionals of a Markov process
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 639-650

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In this paper it was obtained the large deviation principle for the sequence of random processes $Y_n(t)=\frac{1}{n}\int\limits_0^{nt}h(X(u))du,$ where $X(u)$ is a homogeneous Markov process, $h(x)$ is a continuous function, $t \in [0,1]$. In particular, it was proved the large deviation principle for the integral of the telegraph signal process.
Keywords: Large deviations, Markov process, telegraph signal process. 
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     author = {A. V. Logachov and E. I. Prokopenko},
     title = {Large deviation principle for integral functionals of a {Markov} process},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {639--650},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a35/}
}
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A. V. Logachov; E. I. Prokopenko. Large deviation principle for integral functionals of a Markov process. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 639-650. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a35/