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Large Deviations for Scaled Sums of p-Adic-Valued Rotation-Symmetric Independent and Identically Distributed Random Variables

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  • Kumi Yasuda

    (Keio University)

Abstract

The law of an appropriately scaled sum of p-adic-valued, independent, identically and rotation-symmetrically distributed random variables weakly converges to a semi-stable law, if the tail probabilities of the variables satisfy some assumption. If we consider a scaled sum of such random variables with a sufficiently much higher scaling order, it accumulates to the origin, and the mass of any set not including the origin gets small. The purpose of this article is to investigate the asymptotic order of the logarithm of the mass of such sets off the origin. The order is explicitly given under some assumptions on the tail probabilities of the random variables and the scaling order of their sum. It is also proved that the large deviation principle follows with a rate function being constant except at the origin, and the rate function is good only for the case its value is infinity off the origin.

Suggested Citation

  • Kumi Yasuda, 2020. "Large Deviations for Scaled Sums of p-Adic-Valued Rotation-Symmetric Independent and Identically Distributed Random Variables," Journal of Theoretical Probability, Springer, vol. 33(2), pages 1196-1210, June.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:2:d:10.1007_s10959-019-00894-0
    DOI: 10.1007/s10959-019-00894-0
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    References listed on IDEAS

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    1. Frank M. Fossen & Johannes König, 2016. "Personal Bankruptcy Law and Entrepreneurship," ifo DICE Report, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 13(4), pages 28-34, 02.
    2. Khrennikov, Andrei, 2001. "Limit behaviour of sums of independent random variables with respect to the uniform p-adic distribution," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 269-276, February.
    3. Frank M. Fossen & Johannes König, 2016. "Personal Bankruptcy Law and Entrepreneurship," ifo DICE Report, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 13(04), pages 28-34, February.
    4. Kumi Yasuda, 2000. "On Infinitely Divisible Distributions on Locally Compact Abelian Groups," Journal of Theoretical Probability, Springer, vol. 13(3), pages 635-657, July.
    5. ., 2016. "Principles versus pragmatism in law enforcement systems," Chapters, in: Corruption and Criminal Justice, chapter 5, pages 167-205, Edward Elgar Publishing.
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