Bila G. Non-linear Stochastic System Parameter Estimation

New formulations of non-linear parameter identification problems for stochastic systems with weak and strong dependence and methods for their solution are proposed, estimates asymptotic properties and the result application possibilities are investigated in the thesis. Strong consistency and asymptotic normality of periodogram estimates of unknown parameters of almost periodic function in the presence of Gaussian random noise with a weak dependence and in the presence of random noise expressed by functional of Gaussian stationary process with long-range dependence are proven for non-linear stochastic model with continuous time. Two modifications of the periodogram estimation method, depending on the type of functional underlying their computing are investigated. In the case of non-linear stochastic model with continuous time, given by a random field, the strong consistency and asymptotic normality of two-dimensional unknown parameter periodogram estimate of periodic function and the strong consistency of the least-squares estimate of almost periodic function in the presence of random noise given by a functional of a homogeneous Gaussian random field with a long-range dependence are proved. Algorithm for finding the optimal value of the function for solving the identification problems for stochastic systems is proposed.