Geodesic
Construction of the cost and optimal policies in a game problem of stopping of a Markov process
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 164-169 
N. V. Elbakidze. Construction of the cost and optimal policies in a game problem of stopping of a Markov process. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 164-169. http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a15/
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     author = {N. V. Elbakidze},
     title = {Construction of the cost and optimal policies in a~game problem of stopping of {a~Markov} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {164--169},
     year = {1976},
     volume = {21},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a15/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A minimax version of optimal stopping of a Markov process $\{x_n,\mathscr F_n,\mathbf P_x\}$, $n\ge 0$, with a phase space $(E,\mathscr B)$ (a game of two persons with opposite interests) is considered. The process $x_n$ can be stopped at any moment $n\ge 0$. If it is stopped by the first, second or both of the players, the first one gets, correspondingly, a reward $g(x_n)$, $G(x_n)$ or $e(x_n)$. If the process is not stopped, the first player gets reward $\displaystyle\varliminf_{n\to\infty}C(x_n)$. A recurrent procedure of constructing the cost and structure of optimal and $\varepsilon$-optimal stopping times is investigated.