摘要

The problem of optimal random control with the quality quadratic functional for distributed systems with time delay is studied. The system is described by the linear random differential-operator equation, which is not solved for the stochastic differential. The basic assumption is the limitation of the resolvent growth of the characteristic operator sheaf of the equation in some right half-plane. The applications of the abstract results to stochastic partial differential equations, that are not relevant to the Cauchy–Kovalevskaya type, in particular, to the random Navier–Stokes system, are considered.