Geodesic
Invariant measures of Markov chains and Fellerian extensions of chains
Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 496-509

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Sufficient conditions for the existence of non-trivial invariant measures are given both for Feller non-recurrent chains on the locally compact spaces and for the irreducible non-recurrent Markov chains (theorems 3.1, 4.1, 4.2). The second case is reduced to the Fellerian one by means of the construction of a corresponding extension of an initial chain (theorems 1.1, 2.1). 
@article{TVP_1981_26_3_a3,
     author = {M. G. \v{S}ur},
     title = {Invariant measures of {Markov} chains and {Fellerian} extensions of chains},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {496--509},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a3/}
}
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M. G. Šur. Invariant measures of Markov chains and Fellerian extensions of chains. Teoriâ veroâtnostej i ee primeneniâ, Tome 26 (1981) no. 3, pp. 496-509. http://geodesic.mathdoc.fr/item/TVP_1981_26_3_a3/