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Theory of Stochastic Processes, 2017, Volume 22(38), Issue 1, Pages 22–29 (Mi thsp168)  
A note on the Kolmogorov–Marcinkiewicz–Zygmund type strong law of large numbers for elements of autoregression sequences

M. K. Ilienko

Department of Math. Anal. and Probab. Theory, National Technical University of Ukraine (KPI), Peremogy Ave., 37, Kyiv 03056, Ukraine
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Abstract: In the paper we consider the Kolmogorov–Marcinkiewicz–Zygmund type strong law of large numbers for sums whose terms are elements of regression sequences of random variables. Some necessary and sufficient conditions providing SLLN are obtained in terms of coefficients of the regression sequence. Several special cases of regression sequences are considered as well.
Keywords: Kolmogorov–Marcinkiewicz–Zygmund type strong law of large numbers, autoregression sequences of random variables, sums of random variables.
Funding agency Grant number
Swiss National Science Foundation IZ73Z0_152292
Supported by Swiss National Science Foundation, grant No IZ73Z0_152292.
Bibliographic databases:
Document Type: Article
MSC: Primary 60G50, 60B12, 60F15; Secondary 65B10
Language: English
Citation: M. K. Ilienko, “A note on the Kolmogorov–Marcinkiewicz–Zygmund type strong law of large numbers for elements of autoregression sequences”, Theory Stoch. Process., 22(38):1 (2017), 22–29
Citation in format AMSBIB
\Bibitem{Run17}
\by M. K. Ilienko
\paper A note on the Kolmogorov--Marcinkiewicz--Zygmund type strong law of large numbers for elements of autoregression sequences
\jour Theory Stoch. Process.
\yr 2017
\vol 22(38)
\issue 1
\pages 22--29
\mathnet{http://mi.mathnet.ru/thsp168}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3742386}
\zmath{https://zbmath.org/?q=an:1399.60047}
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