Geodesic
Control of Markov processes and $W$-spaces
Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 233-266

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Problems in the control of continuous Markov processes on a semicompactum by two players with conflicting interests are studied. The basic content of the paper is a derivation of Bellman's equations in the case where control is exercised for an infinite time (Theorem 3), and in the case of a problem of optimal stopping (Theorem 6). The results are illustrated by two examples (Theorems 1 and 2). 
@article{IM2_1971_5_1_a14,
     author = {N. V. Krylov},
     title = {Control of  {Markov} processes and $W$-spaces},
     journal = {Izvestiya. Mathematics },
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     volume = {5},
     number = {1},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a14/}
}
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N. V. Krylov. Control of  Markov processes and $W$-spaces. Izvestiya. Mathematics , Tome 5 (1971) no. 1, pp. 233-266. http://geodesic.mathdoc.fr/item/IM2_1971_5_1_a14/