Email this article Nonprobabilistic Infinitely Divisible Distributions: The Lévy-Khinchin Representation, Limit Theorems
- Authors: Platonova M.V.1
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Affiliations:
- St.Petersburg State University
- Issue: Vol 214, No 4 (2016)
- Pages: 517-539
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237446
- DOI: https://doi.org/10.1007/s10958-016-2795-0
- ID: 237446
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Abstract
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
About the authors
M. V. Platonova
St.Petersburg State University
Author for correspondence.
Email: mariyaplat@rambler.ru
Russian Federation, St.Petersburg
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