Geodesic
The Martin boundary for a~portion of a~Markov chain
Matematičeskie zametki, Tome 3 (1968) no. 1, pp. 93-102.

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In this note we study the connection between the Martin boundaries of a non-recurrent Markov chain and its parts. 
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     title = {The {Martin} boundary for a~portion of {a~Markov} chain},
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D. I. Shparo. The Martin boundary for a~portion of a~Markov chain. Matematičeskie zametki, Tome 3 (1968) no. 1, pp. 93-102. http://geodesic.mathdoc.fr/item/MZM_1968_3_1_a11/