Збіжність рядів Баума–Каца для сум елементів лінійних авторегресійних послідовностей $m$-го порядку

M.  Ilienko; A. Polishchuk

doi:10.3842/umzh.v75i9.7340

M. Ilienko National Technical University of Ukraine "Ihor Sikorsky Kyiv Polytechnic Institute"
A. Polishchuk National Technical University of Ukraine "Ihor Sikorsky Kyiv Polytechnic Institute" https://orcid.org/0000-0002-3512-1561

DOI: https://doi.org/10.3842/umzh.v75i9.7340

Keywords: linear m-th order autoregressive sequence, complete convergence, Hsu-Robbins-Erdos series, Spitzer series, Baum-Katz series, weighted sums of random variables

Abstract

UDC 519.21

We establish necessary and sufficient conditions for the convergence of the Baum–Katz series for the sums of elements of linear $m$th order autoregressive sequences of random variables.

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Convergence of Baum–Katz series for sums whose terms are elements of linear $m$ th order autoregressive sequence

Abstract

References