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JOURNALS // Theory of Stochastic Processes // Archive

Theory Stoch. Process., 2010 Volume 16(32), Issue 1, Pages 94–102 (Mi thsp65)

Convergence of independent random variable sum distributions to signed measures and applications to the large deviations problem

N. V. Smorodina, M. M. Faddeev

St. Petersburg State University, St.-Petersburg, Russia

Abstract: 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.

Keywords: Large deviation problem, strictly stable random variable, limit theorems.

MSC: 28C20, 60H05, 60G57

Language: English



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