Geodesic
On~controlled diffusion processes with unbounded coefficients
Izvestiya. Mathematics , Tome 19 (1982) no. 1, pp. 41-64.

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The paper is devoted to the general theory of controlled diffusion processes in a domain of a $d$-dimensional space in the absence of constraints on the growth of the coefficients at infinity. It turned out that the most suitable object of study is the payoff function in the optimal stopping problem for the controlled process. A theory analogous to the theory of controlled processes in the whole space, with growth constraints on the coefficients, is developed under natural assumptions. Bibliography: 16 titles. 
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N. V. Krylov. On~controlled diffusion processes with unbounded coefficients. Izvestiya. Mathematics , Tome 19 (1982) no. 1, pp. 41-64. http://geodesic.mathdoc.fr/item/IM2_1982_19_1_a3/

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

[2] Safonov M. V., “On the control of diffusion processes in a multidimensional cylindrical domain”, Intern. Symp. Stoch. Diff. Eq., Abstr. Comm. (1978, Vilnius), In-t matem. i kibern. Lit. AN, 1978, 168–172

[3] Safonov M. V., “O zadache Dirikhle dlya uravneniya Bellmana v mnogomernoi oblasti”, Dokl. AN SSSR, 253:3 (1980), 535–540 | MR | Zbl

[4] Lions P.-L., “Equations de Hamilton–Jacobi–Bellman dégénérées”, C. R. Acad. Sci. Paris Sér. A-B, 289:5 (1979), A329–A332 | MR

[5] Evans L. C., Friedman A., “Optimal stochastic switching and the Dirichlet problem for the Bellman equation”, Trans. Amer. Math. Soc., 253 (1979), 365–389 | DOI | MR | Zbl

[6] Evans L. C., Second derivative estimates for the Bellman equation, Preprint

[7] Brezis H., Evans L. C., “A variational inequality approach to the Bellman–Dirichlet equation for two elliptic operators”, Rat. Mech. and Anal., 71:1 (1979), 1–13 | DOI | MR | Zbl

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

[9] Krylov N. V., “O traditsionnom vyvode uravneniya Bellmana dlya upravlyaemykh diffuzionnykh protsessov”, Lit. matem. sb., 21:1 (1981), 59–67 | MR

[10] Krylov N. V., “O predelnom perekhode v vyrozhdennykh uravneniyakh Bellmana, I”, Matem. sb., 106:2 (1978), 214–233 | MR | Zbl

[11] Krylov N. V., “O predelnom perekhode v vyrozhdennykh uravneniyakh Bellmana, II”, Matem. sb., 107:1 (1978), 56–68 | MR | Zbl

[12] Evans L. C., “A convergence theorem for solutions of nonlinear second order elliptic equations”, Indiana Univ. Math., J., 27:5 (1978), 875–887 | DOI | MR | Zbl

[13] Krylov N. V., “O predelnom perekhode v parabolicheskikh uravneniyakh Bellmana”, Izv. AN SSSR. Ser. matem., 42:6 (1978), 1418–1425 | MR

[14] Aleksandrov A. D., “Suschestvovanie pochti vezde vtorogo differentsiala vypukloi funktsii i nekotorye svyazannye s nim svoistva vypuklykh poverkhnostei”, Uchenye zapiski LGU, seriya matem., 37, no. 6, 1939, 3–35 | Zbl

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

[16] Danford H., Shvarts Dzh. T., Lineinye operatory, obschaya teoriya, IL, M., 1962