Geodesic
Oh a game connected with a Wiener process
Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 732-735 
S. M. Gusein-Zade. Oh a game connected with a Wiener process. Teoriâ veroâtnostej i ee primeneniâ, Tome 14 (1969) no. 4, pp. 732-735. http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a13/
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     author = {S. M. Gusein-Zade},
     title = {Oh a~game connected with {a~Wiener} process},
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     year = {1969},
     volume = {14},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1969_14_4_a13/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, the following zero-sum game is considered. Two persons are observing a trajectory of a Wiener process in a bounded closed region $E$ with absorbing boundary in a Euclidean $n$-space. One of the players may interrupt the process in a closed region $E_1$ the other in $E_2$. If the process is stopped in a point $x$, then the first player pays to the second one payment $g(x)$. The existence of the payoff function and minimax strategies is proved.