On convergence of Baum-Katz series for elements of linear autoregression

Abstract

We study complete convergence and closely related Hsu-Robbins-Erdős-Spitzer-Baum-Katz series for sums whose terms are elements of linear autoregression sequences. We obtain criterions for convergence of this series expressed in moment assumptions, which for "weakly dependent" sequences are the same as in classical results concerning independent case.