Stochastic optimality in the problem of a linear controller perturbed by a sequence of dependent random variables

A linear discrete time dynamic control system with quadratic cost function perturbed by a sequence of dependent random variables is investigated from the point of view of the so-called probabilistic optimality criteria. In problems of stochastic optimisation, these criteria are related to the study of the asymptotic behaviour (in some probabilistic sense) of an integral cost functional as the horizon of planning tends to infinity. We obtain estimates of the rate of increasing of the defect of the optimal control, that is, the positive part of the difference between values of the cost functional under the optimal control and an arbitrary control, it is shown that these estimates are connected with parameters of the perturbing process. The results are applied to a model of optimal pension funding as a model of dynamic control.