### 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.