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Peculiarities of the large numbers law in conditions of disturbances of statistical stability

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Abstract

Peculiarities of the large numbers law in conditions of disturbances of statistical stability are studied. It is shown that for random sequences the sample mean may converge to a finite number, converge to positive or negative infinity or fluctuate in a fixed interval. A series of theorems are proven, which describe the large numbers law for hyper-random sequence. It is demonstrated that the sample mean in case of a hyper-random quantity may converge to a finite number, converge to a set of finite numbers, fluctuate in non-intersecting intervals of conditional boundaries, fluctuate in unconditional boundaries interval or converge to positive or negative infinity. Differences in convergence types of random and hyper-random sequences should be accounted for when studying radio-engineering devices and systems.

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Authors and Affiliations

  1. Institute of Mathematical Machines and Systems Problems of NAS of Ukraine (IMMSP NASU), Kyiv, Ukraine

    I. I. Gorban

Authors
  1. I. I. Gorban
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Additional information

Original Russian Text © I.I. Gorban, 2011, published in Izv. Vyssh. Uchebn. Zaved., Radioelektron., 2011, Vol. 54, No. 7, pp. 31–42.

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Gorban, I.I. Peculiarities of the large numbers law in conditions of disturbances of statistical stability. Radioelectron.Commun.Syst. 54, 373–383 (2011). https://doi.org/10.3103/S0735272711070053

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  • DOI: https://doi.org/10.3103/S0735272711070053

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