Runovska M. Asymptotic properties of sums of regressive sequences

This thesis is devoted to the investigation of asymptotic behavior of sequences of sums and series of one-dimensional and multi-dimensional linear regressive sequences with independent and symmetric disturbance. In the thesis the conditions for the convergence almost surely of series of regressive sequences in separable Banach spaces, in particulary necessary and sufficient conditions for the convergence almost surely of Gaussian Markov series are obtained. Main results are applied to the problem of finding the Radon-Nykodim density for distributions of Gaussian Markov sequences with admissible shift in sequence spaces.