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The Lévy-Khinchin representation of a class of stable signed measures. (English. Russian original) Zbl 1181.60020
J. Math. Sci., New York 159, No. 3, 363-375 (2009); translation from Zap. Nauchn. Semin. POMI 361, 145-166 (2008).
Summary: We study properties of symmetric stable measures with index of stability \(\alpha \in (2,4)\cup (4,6)\). For such signed measures, we construct a natural analog of the Lévy-Khinchin representation. We show that, in some special sense, these measures are limit measures for sums of independent random variables.

MSC:
60E07 Infinitely divisible distributions; stable distributions
60E05 Probability distributions: general theory
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