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). 
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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/

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