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We study the asymptotic behavior at infinity of the solutions of stochastic functional-differential equations by the method of asymptotic equivalence according to which a system of ordinary differential equations is constructed on the basis of the original stochastic system so that each solution of the stochastic system can be associated with a solution of the constructed deterministic system such that the difference between these solutions tends to zero as t → ∞ both in the mean square and with probability 1. [ABSTRACT FROM AUTHOR]

We consider the optimal control problem for systems with infinite memory whose models are described by functional-differential equations. We prove the theorem on existence, uniqueness, and continuity of solutions for a system of functional-differential equations in which the delay interval is infinitely large. Sufficient conditions for the existence of optimal controls in the optimal control problems for systems with infinite memory are obtained in terms of the right-hand sides of the equations of motion and the function of performance criterion. [ABSTRACT FROM AUTHOR]

We consider the problem of optimal control formed by a parabolic nonlinear equation with rapidly oscillating coefficients, an additive control function, and a coercive cost functional. It is proved that the optimal value of the perturbed problem is close to the optimal value for the corresponding problem with averaged coefficients. [ABSTRACT FROM AUTHOR]

For systems of ordinary differential equations, we obtain some sufficient conditions of existence of an optimal control in terms of their right-hand sides and the cost functional with the use of compactness methods. In the theorems proven, either the time interval is finite and a solution belongs to some domain or the time interval coincides with the semiaxis. [ABSTRACT FROM AUTHOR]