Geodesic
On~control of the solution of a stochastic integral equation with degeneration
Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 249-262

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This paper is devoted to the derivation of Bellman's differential equation in the payoff function $v(x)$ for a broad class of cases (Theorems 1 and 2). We prove that $v(x)$ is the smallest solution of this equation (Theorem 3). 
@article{IM2_1972_6_1_a8,
     author = {N. V. Krylov},
     title = {On~control of the solution of a stochastic integral equation with degeneration},
     journal = {Izvestiya. Mathematics },
     pages = {249--262},
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     volume = {6},
     number = {1},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a8/}
}
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N. V. Krylov. On~control of the solution of a stochastic integral equation with degeneration. Izvestiya. Mathematics , Tome 6 (1972) no. 1, pp. 249-262. http://geodesic.mathdoc.fr/item/IM2_1972_6_1_a8/