Kozyr S. Parametric analysis of stochastic periodic systems in control and identification problems.

Dissertation is devoted to solving problem of diffused approximations of integrals of “physical” white noises, problem of diffused approximations of solutions of differential equations disturbed with “physical” white noises. Discovered estimation of closing in probability in space metric of normalized integral functional of solution of ordinary differential equation with 1-periodical coefficients to the family of Wiener processes. Found estimation of closing speed of solution of ordinary differential equation disturbed with some fast oscillatory centered process build as 1-periodical function of solution of time-homogeneous diffusion equation with 1-periodical coefficients and solution of appropriate Ito equation. Also found estimation of closing speed in case of separated from zero coefficient at “physical” white noise. Solved problem of unknown parameter in drift coefficient of stochastic differential equation with 1-periodical coefficients. Covering interval is built for unknown parameter. It’s limits depend on parameter and observation duration. Found solution of R. Merton problem where risk asset is modeled with P. Samuelson process with fast oscillating periodical stochastic disturbances. Using optimal controls calculated for original R. Merton problem it was shown that effect converges to cost of limit system control. Investor could be satisfied with this suboptimal controls.