Synyavska O. Application of the Baxter sums to estimate parameters of random processes and fields

The thesis is devoted to application of Baxter sums to the estimation of unknown parameters covariance functions of random processes and fields. The strong consistent estimate of the regression coefficient by using Baxter statistics in one model of the observation is obtained and the non-asymptotic confidence regions are constructed. The strong consistent estimate of the parameter covariance function of the fractional anisotropic Wiener field by using Baxter sums is found and the confidence regions are constructed. The Baxter estimate for the unknown parameter covariance function of one non-Gaussian stochastic processes is obtained and the non-asymptotic confidence intervals are found. The Levy-Baxter theorems for one class of non-Gaussian random fields are proved. The strong consistent estimate of the parameter covariance function of one non-Gaussian random fields is obtained.