The theorems about stochastic integral distributions convergence to signed measures and the local limit theorems for large deviations

We study properties of symmetric stable measures with index $\alpha>2$, $\alpha\neq2m$, $m\in\mathbb N$. Such measures are signed ones and hence they are not probability measures. For this class of measures we construct an analogue of the Lévy–Khinchin representation. We show that in some sense these signed measures are limit measures for sums of independent random variables. Bibl. – 11 titles.