This article is cited in 18 papers

On control of the solution of a stochastic integral equation with degeneration

N. V. Krylov


Abstract: 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).

UDC: 519.2

MSC: Primary 60H20, 49C15; Secondary 49A30

Received: 24.12.1970

 English version: Mathematics of the USSR-Izvestiya, 1972, 6:1, 249–262

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