CONVERGENCE OF INDEPENDENT RANDOM VARIABLE SUM DISTRIBUTIONS TO SIGNED MEASURES AND APPLICATIONS TO THE LARGE DEVIATIONS PROBLEM

N. V. SMORODINA AND M. M. FADDEEV

Theory of Stochastic Processes

Vol.16 (32), no.1, 2010, pp.94-102

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.