Geodesic
Principles of potential theory and Markov chains
Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 3, pp. 472-482

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We consider an infinite matrix $G$ with nonnegative entries and with all its columns tending to 0. We investigate those properties of $G$ which allow us to express $G$ in the form $$ G=(I+S+S^2+\dots)A\eqno(1) $$ where $I$ is the identity matrix, $S$ is a substochastic matrix and $A$ is a diagonal matrix with positive entries on the diagonal. These properties are 1) $G$ is nondegenerate in a sense, 2) the vector $e$ with all its components equal to 1 is the limit of an increasing sequence of the potentials of nonnegative measures, 3) the principle of domination holds. These properties are also necessary for representation (1). 
@article{TVP_1966_11_3_a5,
     author = {D. I. Shparo},
     title = {Principles of potential theory and {Markov} chains},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {472--482},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {1966},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1966_11_3_a5/}
}
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D. I. Shparo. Principles of potential theory and Markov chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 3, pp. 472-482. http://geodesic.mathdoc.fr/item/TVP_1966_11_3_a5/