Geodesic
Boundary theory of Markov processes (the discrete case)
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 24 (1969) no. 2, pp. 1-42

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The paper contains a detailed account of the theory of Martin boundaries for Markov processes with a countable number of states and discrete time. The probabilistic method of Hunt is used as a basis. This method is modified so as not to go outside the limits of the usual notion of a Markov process. The generalization of this notion due to Hunt is discussed in the concluding section. 
@article{RM_1969_24_2_a0,
     author = {E. B. Dynkin},
     title = {Boundary theory of {Markov} processes (the discrete case)},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {1--42},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1969_24_2_a0/}
}
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E. B. Dynkin. Boundary theory of Markov processes (the discrete case). Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 24 (1969) no. 2, pp. 1-42. http://geodesic.mathdoc.fr/item/RM_1969_24_2_a0/