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Nonprobabilistic Infinitely Divisible Distributions: The Lévy-Khinchin Representation, Limit Theorems

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Properties of generalized infinitely divisible distributions with Lévy measure \( \varLambda (dx)=\frac{g(x)}{x^{1+\upalpha}}dx, \) α ∈ (2, 4) ∪ (4, 6) are studied. Such a measure is a signed one and, hence, is not a probability measure. It is proved that in some sense these signed measures are the limit measures for the distributions of the sums of independent random variables. Bibliography: 6 titles

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References

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Authors and Affiliations

  1. St.Petersburg State University, St.Petersburg, Russia

    M. V. Platonova

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  1. M. V. Platonova
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Correspondence to M. V. Platonova.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 431, 2014, pp. 145–177.

Translated by I. Ponomarenko.

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Platonova, M.V. Nonprobabilistic Infinitely Divisible Distributions: The Lévy-Khinchin Representation, Limit Theorems. J Math Sci 214, 517–539 (2016). https://doi.org/10.1007/s10958-016-2795-0

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  • DOI: https://doi.org/10.1007/s10958-016-2795-0

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