Geodesic
On sequentially controlled Markov processes
Sbornik. Mathematics, Tome 15 (1971) no. 4, pp. 607-617 
A. K. Zvonkin. On sequentially controlled Markov processes. Sbornik. Mathematics, Tome 15 (1971) no. 4, pp. 607-617. http://geodesic.mathdoc.fr/item/SM_1971_15_4_a7/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider Markov processes with continuous time, where the switching of the controls takes place at random (independent of the future) moments of time. We derive Bellman's cost equation and the existence of $(p,\varepsilon)$ optimal strategies, prove the measurability of cost and give an excessive characterization of cost. Bibliography: 9 titles.

[1] E. B. Dynkin, Markovskie protsessy, Fizmatgiz, Moskva, 1963 | MR

[2] A. N. Shiryaev, Statisticheskii posledovatelnyi analiz (optimalnye pravila ostanovki), Nauka, Moskva, 1969 | MR

[3] D. Blekuell, “Dinamicheskoe programmirovanie v zadachakh s zatukhayuschim deistviem”, Matematika, 11:4 (1967), 151–160

[4] R. E. Shtraukh, “Otritsatelnoe dinamicheskoe programmirovanie”, Matematika, 13:5 (1969), 107–127

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[6] M. A. Naimark, Normirovannye koltsa, Nauka, Moskva, 1968 | MR | Zbl

[7] K. Kuratovskii, Topologiya, t. I, Mir, Moskva, 1966 | MR

[8] E. B. Dynkin, Osnovaniya teorii markovskikh protsessov, Fizmatgiz, Moskva, 1959 | MR

[9] L. Dubins, D. Freedman, “Measurable sets of measures”, Pacific J. Math., 14:4 (1964), 1211–1222 | MR | Zbl