Geodesic
On~control of a~diffusion process up to the time of first exit from a~region
Izvestiya. Mathematics , Tome 19 (1982) no. 2, pp. 297-313.

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The problem of controlling a diffusion process with smooth coefficients up to the time of first exit from a region is reduced to the problem of controlling a diffusion process with smooth coefficients in a whole space. Three examples are considered which show the usefulness of such a reduction in deriving the Bellman equation for the original problem. Bibliography: 12 titles. 
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N. V. Krylov. On~control of a~diffusion process up to the time of first exit from a~region. Izvestiya. Mathematics , Tome 19 (1982) no. 2, pp. 297-313. http://geodesic.mathdoc.fr/item/IM2_1982_19_2_a5/

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[7] Krylov N. V., Upravlyaemye protsessy diffuzionnogo tipa, Nauka, M., 1977 | MR

[8] Krylov N. V., “Ob upravlyaemykh diffuzionnykh protsessakh s neogranichennymi koeffitsientami”, Izv. AN SSSR. Ser. matem., 45:4 (1981), 734–759 | MR | Zbl

[9] Krylov N. V., “Control of the diffusion type processes”, Proc. Internat. Congress Math., v. 2 (Helsinki, 1978), 1980, 859–863 | MR | Zbl

[10] Krylov N. V., “Nekotorye novye rezultaty iz teorii upravlyaemykh diffuzionnykh protsessov”, Matem. sb., 109:1 (1979), 146–164 | MR | Zbl

[11] Krylov N. V., “Obschie metody otsenki proizvodnykh funktsii vyigrysha”, Veroyatnostnye protsessy i upravlenie, Nauka, M., 1978, 94–125 | MR

[12] Cheng Shiu-Yuen, Yau Shing-Tung, “On the regularity of the Monge–Ampère equation $\mathrm{det}(\partial^2u/\partial x_i\partial x_j)=F(x,u)$”, Comm. Pure and Appl. Math., 30:1 (1977), 41–68 | DOI | MR | Zbl