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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