This article is cited in 19 papers

Some new results in the theory of controlled diffusion processes

N. V. Krylov


Abstract: The validity of the Bellman equation for the payoff function for a controlled random diffusion process is proved. The main difference between the results in this article and those known earlier on the same theme is that here no assumptions whatever are made on the nondegeneracy of the controlled process. A theorem on the uniqueness of the solution of the Bellman equation is proved as well. The Bellman equation is examined in a lattice of measures; the derivatives of functions on which it is studied are understood as measures.
Bibliography: 13 titles.

UDC: 519.2+517.9

MSC: Primary 49C10, 60J60; Secondary 35K65

Received: 11.05.1977 and 07.12.1978

 English version: Mathematics of the USSR-Sbornik, 1980, 37:1, 133–149

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