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

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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 criteria for convergence of these series expressed in terms of moment assumptions, which for “weakly dependent” sequences are the same as in classical results concerning the independent case.

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Acknowledgement

The author would like to thank the referee for careful reading and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Peremogy Avenue, 37, 03056, Kyiv, Ukraine

    M. Ilienko

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  1. M. Ilienko
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Correspondence to M. Ilienko.

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Supported by the Grant 0118U003614 from Ministry of Education and Science of Ukraine (project N 2105\(\phi\)).

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Ilienko, M. On the convergence of the Baum--Katz series for elements of a linear autoregression. Acta Math. Hungar. 164, 413–427 (2021). https://doi.org/10.1007/s10474-021-01157-3

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  • DOI: https://doi.org/10.1007/s10474-021-01157-3

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