Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem. (English) Zbl 1224.28032

Smorodina, N. V.; Faddeev, M. M.

Theory Stoch. Process. 16, No. 1, 94-102 (2010).

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

Keywords:

symmetric stable measure; independent random variables; large deviations problem