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Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem. (English) Zbl 1224.28032
Summary: We study properties of symmetric stable measures with index \(\alpha>2,\;\alpha\neq 2k,\;k\in\mathbb{N}\). Such measures are signed ones, and, hence, they are not probability measures. We show that, in some sense, these signed measures are limit measures for sums of independent random variables.

MSC:
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
60H05 Stochastic integrals
60G57 Random measures
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