Limit theorems for a stable sausage

The talk concerns the limit behavior of the volume of a stable sausage defined via a $d$-dimensional rotationally invariant $\alpha$-stable process. I will present a functional central limit theorem (in the case when $d/\alpha>3 /2$) with a standard one-dimensional Brownian motion in the limit and Khintchine's and Chung’s laws of the iterated logarithm (in the case when $d/\alpha>9 /5$). This is a joint work with N. Sandrić and S. Šebek (Uni. Zagreb).