On the convergence of Baum-Katz series for sums of linear 2-nd order autoregressive sequences of random variables

TL;DR

This paper investigates the conditions under which the Baum-Katz series converges for sums of linear second-order autoregressive sequences, extending understanding of convergence in dependent random processes.

Contribution

It provides new sufficient conditions for the convergence of Baum-Katz series specifically for sums of linear second-order autoregressive sequences.

Findings

Established sufficient conditions for series convergence

Extended classical results to dependent autoregressive sequences

Enhanced understanding of complete convergence in autoregressive models

Abstract

We consider complete convergence and closely related Hsu-Robbins-Erdos-Spitzer-Baum-Katz series for sums whose terms are elements of a linear 2-nd order autoregressive sequences of random variables and prove sufficient conditions for the convergence of this series.