On a necessary condition for optimality of a control for stochastic systems. (English. Russian original) Zbl 0621.93076

Shajkhet, L. E.

Theory Probab. Math. Stat. 33, 117-126 (1986); translation from Teor. Veroyatn. Mat. Stat. 33, 104-113 (1985).

A necessary condition is obtained for optimality of a control of the stochastic differential equation \[ d\xi (t)=a(t,\xi (t),u(t))dt+b(t,\xi (t))dw(t)+\int c(z,t,\xi (t)){\tilde \nu}(dt,dz) \] with the quality criterion \[ I(u)=E[F(\xi (T))+\int^{T}_{0}G(s,\xi (s),u(s))ds]. \]

MSC:

93E20	Optimal stochastic control
49K45	Optimality conditions for problems involving randomness
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05	Stochastic integrals

Keywords:

necessary condition; stochastic differential equation