Smorodina, N. V.; Faddeev, M. M. 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. Cited in 1 Document MSC: 60E07 Infinitely divisible distributions; stable distributions 60E05 Probability distributions: general theory Keywords:symmetric stable measures; limit measures for sums of independent random variables PDF BibTeX XML Cite \textit{N. V. Smorodina} and \textit{M. M. Faddeev}, J. Math. Sci., New York 159, No. 3, 363--375 (2009; Zbl 1181.60020); translation from Zap. Nauchn. Semin. POMI 361, 145--166 (2008) Full Text: DOI References: [1] A. V. Skorokhod, Random Processes with Independent Increments [in Russian], Moscow (1986). · Zbl 0622.60082 [2] N. V. Smorodina, ”Asymptotic expansion for the distribution of a smooth homogeneous functional of a strictly stable random vector. II,” Teor. Veroyatn. Primen., 44(2), 458–465 (1999). · Zbl 0982.60003 [3] S. Albeverio and N. Smorodina, ”A distributional approach to multiple stochastic integrals and transformations of the Poisson measure,” Acta Appl. Math., 94, 1–19 (2006). · Zbl 1107.28010 · doi:10.1007/s10440-006-9062-1 [4] I. M. Gelfand and G. E. Shilov, Generalized Functions and Actions on Them [in Russian], Moscow (1958). [5] l. A. lbragimov and Yu. V. Linnik, Independent and Stationary Related Random Values [in Russian], Moscow (1965). [6] M. Sh. Birman and M. Z. Solomyak, Spectral Theory of Self-Adjoint Operators in Hilbert Spaces [in Russian], Leningrad (1980). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.