Geodesic
An estimate of the convergence rate in a~renewal theorem for random variables defined on a~Markov chain
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 3, pp. 563-573

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A sequence of sums of random variables with arbitrary sign defined on transitions of a homogeneous aperiodic discrete Markov chain is represented by Doeblin's method ([2],[3]) as a sequence of sums of independent random variables. The results of [5] being applied, the convergence rate in a renewal theorem ([1]) is estimated. 
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     author = {A. E. Zaslavskii},
     title = {An estimate of the convergence rate in a~renewal theorem for random variables defined on {a~Markov} chain},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     number = {3},
     year = {1972},
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A. E. Zaslavskii. An estimate of the convergence rate in a~renewal theorem for random variables defined on a~Markov chain. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 3, pp. 563-573. http://geodesic.mathdoc.fr/item/TVP_1972_17_3_a15/