Geodesic
Markov decision processes with finite spaces of states and decisions
Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 2, pp. 343-351

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Homogeneous time continuous Markov decision processes with finite spaces of states and decisions and with an additive functional of losses are considered. It is proved that there is an optimal strategy for these processes and that it may be chosen to be a Markov homogeneous one. 
@article{TVP_1966_11_2_a10,
     author = {V. V. Rykov},
     title = {Markov decision processes with finite spaces of states and decisions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {343--351},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {1966},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1966_11_2_a10/}
}
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V. V. Rykov. Markov decision processes with finite spaces of states and decisions. Teoriâ veroâtnostej i ee primeneniâ, Tome 11 (1966) no. 2, pp. 343-351. http://geodesic.mathdoc.fr/item/TVP_1966_11_2_a10/