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Limit theorems for nonnegative independent random variables with truncation

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Abstract

We investigate asymptotic behavior of sums of independent and truncated random variables specified by P (0 \({\leqq X < \infty}\)) = 1 and P \({(X > x) \asymp x^{-\alpha }}\) for \({\alpha > 0}\). By varying truncation levels we study strong laws of large numbers and central limit theorems. These are extensions of the results of Győrfi and Kevei [12] concerning the St. Petersburg game.

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Authors and Affiliations

  1. Department of Mathematics, Fukuoka University of Education, Akama-Bunkyomachi, Munakata, Fukuoka, 811-4192, Japan

    T. Nakata

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  1. T. Nakata
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Correspondence to T. Nakata.

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This research was supported by KAKENHI 21540133 of Japan Society for the Promotion of Science.

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Nakata, T. Limit theorems for nonnegative independent random variables with truncation. Acta Math. Hungar. 145, 1–16 (2015). https://doi.org/10.1007/s10474-014-0474-5

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  • DOI: https://doi.org/10.1007/s10474-014-0474-5

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