Geodesic
The Poisson theorem and the Markov chains
Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 123-125

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It is well-known that the inequality (1) permits to estimate the deviation of some distributions, particularly the binomial distribution, from the Poisson one. We note that this inequality may be naturally extended on the case of Markov chains. Two examples are considered. 
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     author = {M. G. \v{S}ur},
     title = {The {Poisson} theorem and the {Markov} chains},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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M. G. Šur. The Poisson theorem and the Markov chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 29 (1984) no. 1, pp. 123-125. http://geodesic.mathdoc.fr/item/TVP_1984_29_1_a12/