Sakhno L. Asymptotic and spectral methods for statistical estimation of random processes and fields

In the thesis methods of statistical and spectral analysis of random processes and fields are developed. Limit theorems are stated for the empirical spectral functionals for the stationary processes and fields. Methods for statistical parameter estimation of stationary processes and fields are developed basing on the use of spectral densities of the second and higher orders. The limit distributions are obtained for the Kaplan-Meier estimator for data with strong dependence. Spectral densities are derived for random fields related to solutions of partial differential equations with random initial conditions. Spectral representations of tensor random fields on the sphere are obtained.